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  • 1. Aczel, Peter
    et al.
    Crosilla, Laura
    Ishihara, Hajime
    Palmgren, Erik
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Schuster, Peter
    Binary refinement implies discrete exponentiation2006In: Studia Logica, Vol. 84, p. 361-368Article in journal (Refereed)
  • 2.
    Ageev, Dmitry S.
    et al.
    Russian Acad Sci, Dept Math Methods Quantum Technol, Steklov Math Inst, Gubkin Str 8, Moscow 119991, Russia..
    Bagrov, Andrey A.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Iliasov, Askar A.
    Radboud Univ Nijmegen, Inst Mol & Mat, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands..
    Coleman-Weinberg potential in p-adic field theory2020In: European Physical Journal C, ISSN 1434-6044, E-ISSN 1434-6052, Vol. 80, no 9, article id 859Article in journal (Refereed)
    Abstract [en]

    In this paper, we study lambda phi(4) scalar field theory defined on the unramified extension of p-adic numbers Q(pn). For different "space-time" dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, p -> 1 and p -> infinity. We show that the p -> 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the p -> infinity limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.

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  • 3.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    A zero-one law for l-colourable structures with a vectorspace pregeometry2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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  • 4.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Homogenizable structures and model completeness2016In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, no 7-8, p. 977-995Article in journal (Refereed)
    Abstract [en]

    A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

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  • 5.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    >k-homogeneous infinite graphs2018In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, p. 160-174Article in journal (Refereed)
    Abstract [en]

    In this article we give an explicit classification for the countably infinite graphs G which are, for some k, ≥k-homogeneous. It turns out that a ≥k  -homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.

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  • 6.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Limit Laws, Homogenizable Structures and Their Connections2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is in the field of mathematical logic and especially model theory. The thesis contain six papers where the common theme is the Rado graph R. Some of the interesting abstract properties of R are that it is simple, homogeneous (and thus countably categorical), has SU-rank 1 and trivial dependence. The Rado graph is possible to generate in a probabilistic way. If we let K be the set of all finite graphs then we obtain R as the structure which satisfy all properties which hold with assymptotic probability 1 in K. On the other hand, since the Rado graph is homogeneous, it is also possible to generate it as a Fraïssé-limit of its age.

    Paper I studies the binary structures which are simple, countably categorical, with SU-rank 1 and trivial algebraic closure. The main theorem shows that these structures are all possible to generate using a similar probabilistic method which is used to generate the Rado graph. Paper II looks at the simple homogeneous structures in general and give certain technical results on the subsets of SU-rank 1.

    Paper III considers the set K consisting of all colourable structures with a definable pregeometry and shows that there is a 0-1 law and almost surely a unique definable colouring. When generating the Rado graph we almost surely have only rigid structures in K. Paper IV studies what happens if the structures in K are only the non-rigid finite structures. We deduce that the limit structures essentially try to stay as rigid as possible, given the restriction, and that we in general get a limit law but not a 0-1 law.

    Paper V looks at the Rado graph's close cousin the random t-partite graph and notices that this structure is not homogeneous but almost homogeneous. Rather we may just add a definable binary predicate, which hold for any two elemenets which are in the same part, in order to make it homogeneous. This property is called being homogenizable and in Paper V we do a general study of homogenizable structures. Paper VI conducts a special case study of the homogenizable graphs which are the closest to being homogeneous, providing an explicit classification of these graphs.

    List of papers
    1. Simple structures axiomatized by almost sure theories
    Open this publication in new window or tab >>Simple structures axiomatized by almost sure theories
    2016 (English)In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, no 5, p. 435-456Article in journal (Refereed) Published
    Abstract [en]

    In this article we give a classification of the binary, simple, ω-categorical structures with SU-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as ω-stability or strong minimality.

    Keywords
    Random structure, Almost sure theory, Pregeometry, Supersimple, Countably categorical
    National Category
    Algebra and Logic
    Research subject
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-276995 (URN)10.1016/j.apal.2016.02.001 (DOI)000372680500001 ()
    Available from: 2016-03-01 Created: 2016-02-17 Last updated: 2017-11-30Bibliographically approved
    2. On sets with rank one in simple homogeneous structures
    Open this publication in new window or tab >>On sets with rank one in simple homogeneous structures
    2015 (English)In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, p. 223-250Article in journal (Refereed) Published
    Abstract [en]

    We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

    Keywords
    model theory, homogeneous structure, simple theory, pregeometry, rank, reduct, random structure
    National Category
    Algebra and Logic
    Research subject
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-243006 (URN)10.4064/fm228-3-2 (DOI)000352858400002 ()
    Available from: 2015-02-03 Created: 2015-02-03 Last updated: 2017-12-05Bibliographically approved
    3. Random l-colourable structures with a pregeometry
    Open this publication in new window or tab >>Random l-colourable structures with a pregeometry
    2017 (English)In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, no 1-2, p. 32-58Article in journal (Refereed) Published
    Abstract [en]

    We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

    Place, publisher, year, edition, pages
    Wiley-VCH Verlagsgesellschaft, 2017
    National Category
    Algebra and Logic
    Research subject
    Mathematical Logic
    Identifiers
    urn:nbn:se:uu:diva-321515 (URN)10.1002/malq.201500006 (DOI)000400361900003 ()
    Available from: 2017-05-06 Created: 2017-05-06 Last updated: 2017-11-28Bibliographically approved
    4. Limit laws and automorphism groups of random nonrigid structures
    Open this publication in new window or tab >>Limit laws and automorphism groups of random nonrigid structures
    2015 (English)In: Journal of Logic and Analysis, E-ISSN 1759-9008, Vol. 7, no 2, p. 1-53, article id 1Article in journal (Refereed) Published
    Abstract [en]

    A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

    Keywords
    finite model theory, limit law, zero-one law, random structure, automorphism group
    National Category
    Algebra and Logic
    Research subject
    Mathematical Logic
    Identifiers
    urn:nbn:se:uu:diva-248078 (URN)10.4115/jla.2015.7.2 (DOI)000359802400001 ()
    Available from: 2015-03-26 Created: 2015-03-26 Last updated: 2023-10-02Bibliographically approved
    5. Homogenizable structures and model completeness
    Open this publication in new window or tab >>Homogenizable structures and model completeness
    2016 (English)In: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, no 7-8, p. 977-995Article in journal (Refereed) Published
    Abstract [en]

    A homogenizable structure M is a structure where we may add a finite amount of new relational symbols to represent some 0-definable relations in order to make the structure homogeneous. In this article we will divide the homogenizable structures into different classes which categorize many known examples and show what makes each class important. We will show that model completeness is vital for the relation between a structure and the amalgamation bases of its age and give a necessary and sufficient condition for an countably categorical model-complete structure to be homogenizable.

    Keywords
    Homogenizable, Model-complete, Amalgamation class, Quantifier-elimination
    National Category
    Algebra and Logic
    Research subject
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-303714 (URN)10.1007/s00153-016-0507-6 (DOI)000385155700010 ()
    Available from: 2016-09-22 Created: 2016-09-22 Last updated: 2017-11-28Bibliographically approved
    6. >k-homogeneous infinite graphs
    Open this publication in new window or tab >>>k-homogeneous infinite graphs
    2018 (English)In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, p. 160-174Article in journal (Refereed) Published
    Abstract [en]

    In this article we give an explicit classification for the countably infinite graphs G which are, for some k, ≥k-homogeneous. It turns out that a ≥k  -homogeneous graph M is non-homogeneous if and only if it is either not 1-homogeneous or not 2-homogeneous, both cases which may be classified using ramsey theory.

    Keywords
    >k-homomogeneous, countably infinite graph
    National Category
    Algebra and Logic
    Research subject
    Mathematical Logic
    Identifiers
    urn:nbn:se:uu:diva-329362 (URN)10.1016/j.jctb.2017.08.007 (DOI)000417771100009 ()
    Available from: 2017-09-26 Created: 2017-09-26 Last updated: 2018-04-05Bibliographically approved
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  • 7.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Simple structures axiomatized by almost sure theories2016In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, no 5, p. 435-456Article in journal (Refereed)
    Abstract [en]

    In this article we give a classification of the binary, simple, ω-categorical structures with SU-rank 1 and trivial algebraic closure. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of finite structures equipped with a probability measure. This study give results about general almost sure theories, but also considers certain attributes which, if they are almost surely true, generate almost sure theories with very specific properties such as ω-stability or strong minimality.

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  • 8.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    To infinity and back: Logical limit laws and almost sure theories2014Licentiate thesis, comprehensive summary (Other academic)
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  • 9.
    Ahlman, Ove
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Limit laws and automorphism groups of random nonrigid structures2015In: Journal of Logic and Analysis, E-ISSN 1759-9008, Vol. 7, no 2, p. 1-53, article id 1Article in journal (Refereed)
    Abstract [en]

    A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of finite structures with increasingly more complex automorphism groups. Such a hierarchy can be defined in more than one way. For example, the kth level of the hierarchy can consist of all structures having at least k elements which are moved by some automorphism. Or we can consider, for any finite group G, all finite structures M such that G is a subgroup of the group of automorphisms of M; in this case the "hierarchy" is a partial order. In both cases, as well as variants of them, each "level" satisfies a logical limit law, but not a zero-one law (unless k = 0 or G is trivial). Moreover, the number of (labelled or unlabelled) n-element structures in one place of the hierarchy divided by the number of n-element structures in another place always converges to a rational number or to infinity as n -> infinity. All instances of the respective result are proved by an essentially uniform argument.

    Download full text (pdf)
    fulltext
  • 10.
    Ahlman, Ove
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    On sets with rank one in simple homogeneous structures2015In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, p. 223-250Article in journal (Refereed)
    Abstract [en]

    We study definable sets D of SU-rank 1 in Meq, where M is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such D can be seen as a 'canonically embedded structure', which inherits all relations on D which are definable in Meq, and has no other definable relations. Our results imply that if no relation symbol of the language of M has arity higher than 2, then there is a close relationship between triviality of dependence and D being a reduct of a binary random structure. Somewhat more precisely: (a) if for every n≥2, every n-type p(x1,...,xn) which is realized in D is determined by its sub-2-types q(xi,xj)⊆p, then the algebraic closure restricted to D is trivial; (b) if M has trivial dependence, then D is a reduct of a binary random structure.

    Download full text (pdf)
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  • 11.
    Ahlman, Ove
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Koponen, Vera
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Random l-colourable structures with a pregeometry2017In: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, no 1-2, p. 32-58Article in journal (Refereed)
    Abstract [en]

    We study finite -colourable structures with an underlying pregeometry. The probability measure that is usedcorresponds to a process of generating such structures by which colours are first randomly assigned to all1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions aresatisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure,where we now forget the specific colouring of the generating process, has a given property. With this measurewe get the following results: (1) A zero-one law. (2) The set of sentences with asymptotic probability 1 has anexplicit axiomatisation which is presented. (3) There is a formula ξ (x, y) (not directly speaking about colours)such that, with asymptotic probability 1, the relation “there is an -colouring which assigns the same colourto x and y” is defined by ξ (x, y). (4) With asymptotic probability 1, an -colourable structure has a unique-colouring (up to permutation of the colours).

  • 12.
    Ahlsén, Daniel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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  • 13.
    Ahlsén, Daniel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Limitless Analysis2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 14.
    Ahmed, Chwas
    et al.
    Univ Sulaimani, Coll Sci, Dept Math, Sulaymaniyah, Kurdistan, Iraq.;Univ Leeds, Sch Math, Leeds, England..
    Martin, Paul
    Univ Leeds, Sch Math, Leeds, England..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Tonal partition algebras: fundamental and geometrical aspects of representation theory2024In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 52, no 1, p. 233-271Article in journal (Refereed)
    Abstract [en]

    For l, n is an element of N we define tonal partition algebra P-l (n) over Z[delta]. We construct modules {Delta mu} mu for P-l (n) over Z[delta], and hence over any integral domain containing Z[delta] (such as C[delta]), that pass to a complete set of irreducible modules over the field of fractions. We show that P-l (n) is semisimple there. That is, we construct for the tonal partition algebras a modular system in the sense of Brauer. Using a "geometrical" index set for the Delta-modules, we give an order with respect to which the decomposition matrix over C (with d. C-x) is upper-unitriangular. We establish several crucial properties of the Delta-modules. These include a tower property, with respect to n, in the sense of Green and Cox-Martin-Parker-Xi; contravariant forms with respect to a natural involutive antiautomorphism; a highest weight category property; and branching rules.

  • 15.
    Al Homsi, Rania
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Equation Solving in Indian Mathematics2018Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 16.
    Al-Ayyoub, Ibrahim
    et al.
    Sultan Qaboos University; Jordan University of Science and Technology.
    Nasernejad, Mehrdad
    Ferdowsi University of Mashhad.
    Khashyarmanesh, Kazem
    Ferdowsi University of Mashhad.
    Roberts, Leslie G.
    Queen's University.
    Crispin Quiñonez, Veronica
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Results on the normality of square-free monomial ideals and cover ideals under some graph operations2021In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 127, no 3, p. 441-457Article in journal (Refereed)
    Abstract [en]

    In this paper, we introduce techniques for producing normal square-free monomial ideals fromold such ideals. These techniques are then used to investigate the normality of cover ideals undersome graph operations. Square-free monomial ideals that come out as linear combinations of twonormal ideals are shown to be not necessarily normal; under such a case we investigate the integralclosedness of all powers of these ideals.

  • 17.
    Ali, Hassan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Exceptional Groups and their Generators2022Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Exceptional algebraic groups are divided into five types, namely G2, F4,E6, E7 and E8. In this thesis we discuss G2, F4 and E6. We discuss the exceptionalalgebraic groups via octonion algebras and Jordan algebras. We firstconsider the groups of type G2. Groups of type G2 are automorphism groupsof octonion algebras, a form of composition algebras. We take the algebra of Zorn vector matrices and find the possible values of automorphisms of thisalgebra with the help of U-operators. We also discuss the product of two andthree U-operators. Then we discuss Albert algebras, since groups of type E6and F4 are related to these algebras. The Albert algebras are a form of Jordanalgebras. We also study the U-operators in Albert algebras. In this thesis wework over algebraically closed fields of characteristic zero.

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  • 18.
    Alpan, Gökalp
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Partial Differential Equations.
    Kozhan, Rostyslav
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Partial Differential Equations.
    Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles2022In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 63, no 4, article id 043505Article in journal (Refereed)
    Abstract [en]

    We compute the joint eigenvalue distribution for the rank one Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles (beta > 0) of random matrices.

  • 19.
    Alsaody, Seidon
    Department of Mathematical and Statistical Sciences, University of Alberta, AB, Canada.
    Albert algebras over rings and related torsors2020In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-4279, Vol. 73, no 3, p. 875-898Article in journal (Refereed)
    Abstract [en]

    We study exceptional Jordan algebras and related exceptional group schemes over commutative rings from a geometric point of view, using appropriate torsors to parametrize and explain classical and new constructions, and proving that over rings, they give rise to nonisomorphic structures.

    We begin by showing that isotopes of Albert algebras are obtained as twists by a certain  F4-torsor with total space a group of type  E6  and, using this, that Albert algebras over rings in general admit nonisomorphic isotopes even in the split case, as opposed to the situation over fields. We then consider certain  D4 -torsors constructed from reduced Albert algebras, and show how these give rise to a class of generalised reduced Albert algebras constructed from compositions of quadratic forms. Showing that this torsor is nontrivial, we conclude that the Albert algebra does not uniquely determine the underlying composition, even in the split case. In a similar vein, we show that a given reduced Albert algebra can admit two coordinate algebras which are nonisomorphic and have nonisometric quadratic forms, contrary, in a strong sense, to the case over fields, established by Albert and Jacobson.

  • 20.
    Alsaody, Seidon
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2012Report (Other academic)
    Abstract [en]

    A condition for when two eight-dimensional absolute valued algebras are isomorphic was given in [4]. We use this condition to deduce a description (in the sense of Dieterich, [9]) of the category of such algebras, and show how previous descriptions of some full subcategories fit in this description. Led by the structure of these examples, we aim at systematically constructing new subcategories whose classification is manageable. To this end we propose, in greater generality, the definition of sharp stabilizers for group actions, and use these to obtain conditions for when certain subcategories of groupoids are full. This we apply to the category of eight-dimensional absolute valued algebras and obtain a class of subcategories, for which we simplify, and partially solve, the classification problem.

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  • 21.
    Alsaody, Seidon
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Morphisms in the Category of Finite Dimensional Absolute Valued Algebras2011Report (Other academic)
    Abstract [en]

    This is a study of morphisms in the category of nite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classication of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms from two-dimensional algebras we describe the orbits under the actions of the automorphism groups involved. Parts of these descriptions rely on a suitable choice of a cross-section of four-dimensional absolute valued algebras, and we thus end by providing an explicit means of transferring these results to algebras outside this crosssection.

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  • 22.
    Alsaody, Seidon
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    On Finite-Dimensional Absolute Valued Algebras2012Licentiate thesis, comprehensive summary (Other academic)
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  • 23.
    Alsaody, Seidon
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Chernousov, Vladimir
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
    Pianzola, Arturo
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.;Ctr Altos Estudios Ciencias Exactas, Ave Mayo 866, RA-1084 Buenos Aires, DF, Argentina..
    On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E-7,1(78) and E-8,2(78) (With an Appendix by R. M. Weiss)2021In: Forum of Mathematics, Sigma, ISSN 2050-5094, Vol. 9, article id e75Article in journal (Refereed)
    Abstract [en]

    We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the TitsWeiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E-7,1(78), E-8,2(78). As a further corollary, we show that some standard conjectures on the groups of R-equivalence classes in algebraic groups and the norm principle are true for strongly inner forms of type E-1(6).

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  • 24.
    Alsätra, Tova
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Knots, Reidemeister Moves and Knot Invariants2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 25.
    Alverbro, Miranda
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    An Overwiev Of The Rado Graph2022Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This paper examines the Rado graph, the unique, countably infinite, universalgraph. Many of the central properties are covered in detail, and various constructionsare provided, using results from a variety of fields of mathematics. A variantof the Rado graph was initially constructed by Ackermann. The actual Rado graphwas studied later, by Erdős and Rényi, before Rado rediscovered it from a differentperspective. A multitude of other authors have since then contributed to the subject.

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  • 26.
    Andersson, Anders
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    On second-order generalized quantifiers and finite structures2002In: Ann. Pure Appl. Logic, Vol. 115, no 1-3, p. 1-32Article in journal (Refereed)
  • 27.
    Andersson, Evelina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Random sampling of finite graphs with constraints2014Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
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  • 28. Armstrong, Alasdair
    et al.
    Struth, Georg
    Weber, Tjark
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Programming and automating mathematics in the Tarski-Kleene hierarchy2014In: Journal of Logical and Algebraic Methods in Programming, ISSN 2352-2208, Vol. 83, no 2, p. 87-102Article in journal (Refereed)
    Abstract [en]

    We present examples from a reference implementation of variants of Kleene algebras and Tarski's relation algebras in the theorem proving environment Isabelle/HOL. For Kleene algebras we show how models can be programmed, including sets of traces and paths, languages, binary relations, max-plus and min-plus algebras, matrices, formal power series. For relation algebras we discuss primarily proof automation in a comprehensive library and present an advanced formalisation example. 

  • 29.
    Asplund, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Linking and Morse Theory2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 30.
    Asplund, Teo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Extremal Hypergraphs2013Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 31.
    Awodey, Steve
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Eliasson, Jonas
    Ultrasheaves and double negation2002Report (Other scientific)
  • 32. Awodey, Steve
    et al.
    Eliasson, Jonas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Ultrasheaves and double negation2004In: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 45, no 4, p. 235-245Article in journal (Refereed)
    Abstract [en]

    Moerdijk has introduced a topos of sheaves on a category of filters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultrafilters—the ultrasheaves. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on filters.

  • 33.
    Bai, Zhong-Zhi
    et al.
    Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China..
    Neytcheva, Maya
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
    Reichel, Lothar
    Kent State Univ, Dept Math Sci, Kent, OH 44242 USA..
    Editorial: Novel methods and theories in numerical algebra with interdisciplinary applications2018In: Numerical Linear Algebra with Applications, ISSN 1070-5325, E-ISSN 1099-1506, Vol. 25, no 4, article id e2181Article in journal (Other academic)
  • 34.
    Bengtsson, Niclas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Abstract Logics and Lindström's Theorem2023Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A definition of abstract logic is presented. This is used to explore and compare some abstract logics, such as logics with generalised quantifiers and infinitary logics, and their properties. Special focus is given to the properties of completeness, compactness, and the Löwenheim-Skolem property. A method of comparing different logics is presented and the concept of equivalent logics introduced. Lastly a proof is given for Lindström's theorem, which provides a characterization of elementary logic, also known as first-order logic, as the strongest logic for which both the compactness property and the Löwenheim-Skolem property, holds.

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  • 35.
    Berg, Sandra
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Global dimension of (higher) Nakayama algebras2020Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
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  • 36.
    Berg, Sandra
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Om talet Π2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 37.
    Berglund, Björn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Arkimedes metod2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 38.
    Bjerkeng van Keppel, Alvar
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    The Unprovability of the Continuum Hypothesis Using the Method of Forcing2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 39.
    Björklund, Johan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Flexible isotopy classification of flexible links2016In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, no 8, article id 1650049Article in journal (Refereed)
    Abstract [en]

    In this paper, we define and study flexible links and flexible isotopy in RP3 subset of CP3. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholm's interpretation of Viro's encomplexed writhe.

  • 40.
    Blanck, J
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Stoltenberg-Hansen, V
    Tucker, J.V.
    Domain representations of partial functions, with applications to spatial objects and contructive volume geometry2001Report (Other scientific)
  • 41.
    Blanck, Jens
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Stoltenberg-Hansen, Viggo
    Tucker, John V.
    Domain representations of partial functions, with applications to spatial objects and constructive volume geometry2002In: Theoret. Comput. Sci., Vol. 284, no 2, p. 207-240Article in journal (Refereed)
  • 42.
    Block, Max
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Undecidability of finite satisfiability and characterization of NP in finite model theory2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 43.
    Blomqvist, Christer
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Miniräknarmania: eller hur att få ut så mycket som möjligt från en enkel reklamräknare2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 44.
    Bocca, Gabriele
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Quasi-hereditary covers of higher zigzag algebras of type A2021In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 225, no 1, article id 106466Article in journal (Refereed)
    Abstract [en]

    In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Delta, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Delta-Koszul dual as the path algebra of a quiver with relations. (C) 2020 Elsevier B.V. All rights reserved.

  • 45.
    Briggs, Benjamin
    et al.
    Univ Copenhagen, Dept Math Sci, Copenhagen, Denmark..
    Rubio y Degrassi, Lleonard
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    On the Lie algebra structure of integrable derivations2023In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 55, no 6, p. 2617-2634Article in journal (Refereed)
    Abstract [en]

    Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra A forms a Lie algebra, and a restricted Lie algebra if A contains a field of characteristic p. We deduce that the space of integrable classes in HH1 (A) forms a (restricted) Lie algebra that is invariant under derived equivalences, and under stable equivalences of Morita type between self-injective algebras. We also provide negative answers to questions about integrable derivations posed by Linckelmann and by Farkas, Geiss and Marcos. Along the way, we compute the first Hochschild cohomology of the group algebra of any symmetric group.

  • 46.
    Briggs, Benjamin
    et al.
    Univ Copenhagen, Dept Math Sci, Copenhagen, Denmark..
    Rubio y Degrassi, Lleonard
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Stable invariance of the restricted Lie algebra structure of Hochschild cohomology2022In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 321, no 1, p. 45-71Article in journal (Refereed)
    Abstract [en]

    We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby, we obtain a number of positive characteristic stable invariants, such as the p-toral rank of HH1(A, A). We also prove a more general result concerning Iwanaga-Gorenstein algebras, using a generaliza-tion of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory.These results are proven by first establishing the stable invariance of the B∞-structure of the Hochschild cochain complex. In the appendix, we explain how the p-power operation on Hochschild cohomology can be seen as an artifact of this B∞-structure. In particular, we establish well-definedness of the p-power operation, following some-originally topological-methods due to May, Cohen and Turchin, using the language of operads.

  • 47.
    Brzezinski, Tomasz
    et al.
    Swansea Univ, Dept Math, Bay Campus,Fabian Way, Swansea SA1 8EN, W Glam, Wales.;Univ Bialystok, Fac Math, K Ciolkowskiego 1M, PL-15245 Bialystok, Poland..
    Koenig, Steffen
    Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70569 Stuttgart, Germany..
    Külshammer, Julian
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    From quasi-hereditary algebras with exact Borel subalgebras to directed bocses2020In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 52, no 2, p. 367-378Article in journal (Refereed)
    Abstract [en]

    Up to Morita equivalence, every quasi-hereditary algebra is the dual algebra of a directed bocs or a coring. From the bocs, an exact Borel subalgebra is obtained. In this paper a characterisation of exact Borel subalgebras arising in this way is given.

  • 48.
    Buciumas, Valentin
    et al.
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB, Canada.
    Ko, Hankyung
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Logic and Representation Theory.
    Polynomial functors and two-parameter quantum symmetric pairs2023In: Transformation groups, ISSN 1083-4362, E-ISSN 1531-586X, Vol. 28, no 1, p. 107-149Article in journal (Refereed)
    Abstract [en]

    We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups GLn, the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair (UBQ,q(gln), Uq(gln)) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra UBQ,q(gln) appears in a Schur–Weyl duality with the type B Hecke algebra HBQ,q(d). We endow two-parameter polynomial functors with a cylinder braided structure which we use to construct the two-parameter Schur functors. Our polynomial functors can be precomposed with the quantum polynomial functors of type A producing new examples of action pairs.

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  • 49.
    Bäck, Viktor
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Localization of Multiscale Screened Poisson Equation2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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  • 50.
    Carlbaum, Wilhelm
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Primtal och kryptografi2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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