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  • 1. Aczel, Peter
    et al.
    Crosilla, Laura
    Ishihara, Hajime
    Palmgren, Erik
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Schuster, Peter
    Binary refinement implies discrete exponentiation2006Inngår i: Studia Logica, Vol. 84, s. 361-368Artikkel i tidsskrift (Fagfellevurdert)
  • 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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Fysiska sektionen, Institutionen för fysik och astronomi, Materialteori.
    Iliasov, Askar A.
    Radboud Univ Nijmegen, Inst Mol & Mat, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands..
    Coleman-Weinberg potential in p-adic field theory2020Inngår i: European Physical Journal C, ISSN 1434-6044, E-ISSN 1434-6052, Vol. 80, nr 9, artikkel-id 859Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    FULLTEXT01
  • 3.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    A zero-one law for l-colourable structures with a vectorspace pregeometry2012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 4.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Homogenizable structures and model completeness2016Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, nr 7-8, s. 977-995Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 5.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    >k-homogeneous infinite graphs2018Inngår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, s. 160-174Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 6.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Limit Laws, Homogenizable Structures and Their Connections2018Doktoravhandling, med artikler (Annet vitenskapelig)
    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.

    Delarbeid
    1. Simple structures axiomatized by almost sure theories
    Åpne denne publikasjonen i ny fane eller vindu >>Simple structures axiomatized by almost sure theories
    2016 (engelsk)Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, nr 5, s. 435-456Artikkel i tidsskrift (Fagfellevurdert) 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.

    Emneord
    Random structure, Almost sure theory, Pregeometry, Supersimple, Countably categorical
    HSV kategori
    Forskningsprogram
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-276995 (URN)10.1016/j.apal.2016.02.001 (DOI)000372680500001 ()
    Tilgjengelig fra: 2016-03-01 Laget: 2016-02-17 Sist oppdatert: 2017-11-30bibliografisk kontrollert
    2. On sets with rank one in simple homogeneous structures
    Åpne denne publikasjonen i ny fane eller vindu >>On sets with rank one in simple homogeneous structures
    2015 (engelsk)Inngår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 223-250Artikkel i tidsskrift (Fagfellevurdert) 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.

    Emneord
    model theory, homogeneous structure, simple theory, pregeometry, rank, reduct, random structure
    HSV kategori
    Forskningsprogram
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-243006 (URN)10.4064/fm228-3-2 (DOI)000352858400002 ()
    Tilgjengelig fra: 2015-02-03 Laget: 2015-02-03 Sist oppdatert: 2017-12-05bibliografisk kontrollert
    3. Random l-colourable structures with a pregeometry
    Åpne denne publikasjonen i ny fane eller vindu >>Random l-colourable structures with a pregeometry
    2017 (engelsk)Inngår i: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, nr 1-2, s. 32-58Artikkel i tidsskrift (Fagfellevurdert) 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).

    sted, utgiver, år, opplag, sider
    Wiley-VCH Verlagsgesellschaft, 2017
    HSV kategori
    Forskningsprogram
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-321515 (URN)10.1002/malq.201500006 (DOI)000400361900003 ()
    Tilgjengelig fra: 2017-05-06 Laget: 2017-05-06 Sist oppdatert: 2017-11-28bibliografisk kontrollert
    4. Limit laws and automorphism groups of random nonrigid structures
    Åpne denne publikasjonen i ny fane eller vindu >>Limit laws and automorphism groups of random nonrigid structures
    2015 (engelsk)Inngår i: Journal of Logic and Analysis, E-ISSN 1759-9008, Vol. 7, nr 2, s. 1-53, artikkel-id 1Artikkel i tidsskrift (Fagfellevurdert) 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.

    Emneord
    finite model theory, limit law, zero-one law, random structure, automorphism group
    HSV kategori
    Forskningsprogram
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-248078 (URN)10.4115/jla.2015.7.2 (DOI)000359802400001 ()
    Tilgjengelig fra: 2015-03-26 Laget: 2015-03-26 Sist oppdatert: 2023-10-02bibliografisk kontrollert
    5. Homogenizable structures and model completeness
    Åpne denne publikasjonen i ny fane eller vindu >>Homogenizable structures and model completeness
    2016 (engelsk)Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 55, nr 7-8, s. 977-995Artikkel i tidsskrift (Fagfellevurdert) 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.

    Emneord
    Homogenizable, Model-complete, Amalgamation class, Quantifier-elimination
    HSV kategori
    Forskningsprogram
    Matematik
    Identifikatorer
    urn:nbn:se:uu:diva-303714 (URN)10.1007/s00153-016-0507-6 (DOI)000385155700010 ()
    Tilgjengelig fra: 2016-09-22 Laget: 2016-09-22 Sist oppdatert: 2017-11-28bibliografisk kontrollert
    6. >k-homogeneous infinite graphs
    Åpne denne publikasjonen i ny fane eller vindu >>>k-homogeneous infinite graphs
    2018 (engelsk)Inngår i: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 128, s. 160-174Artikkel i tidsskrift (Fagfellevurdert) 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.

    Emneord
    >k-homomogeneous, countably infinite graph
    HSV kategori
    Forskningsprogram
    Matematisk logik
    Identifikatorer
    urn:nbn:se:uu:diva-329362 (URN)10.1016/j.jctb.2017.08.007 (DOI)000417771100009 ()
    Tilgjengelig fra: 2017-09-26 Laget: 2017-09-26 Sist oppdatert: 2018-04-05bibliografisk kontrollert
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  • 7.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Simple structures axiomatized by almost sure theories2016Inngår i: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 167, nr 5, s. 435-456Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 8.
    Ahlman, Ove
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    To infinity and back: Logical limit laws and almost sure theories2014Licentiatavhandling, med artikler (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 9.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limit laws and automorphism groups of random nonrigid structures2015Inngår i: Journal of Logic and Analysis, E-ISSN 1759-9008, Vol. 7, nr 2, s. 1-53, artikkel-id 1Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 10.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On sets with rank one in simple homogeneous structures2015Inngår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 228, s. 223-250Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 11.
    Ahlman, Ove
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Koponen, Vera
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Random l-colourable structures with a pregeometry2017Inngår i: Mathematical logic quarterly, ISSN 0942-5616, E-ISSN 1521-3870, Vol. 63, nr 1-2, s. 32-58Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Classifying Categories: The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories2018Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 13.
    Ahlsén, Daniel
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Limitless Analysis2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    Tonal partition algebras: fundamental and geometrical aspects of representation theory2024Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 52, nr 1, s. 233-271Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Equation Solving in Indian Mathematics2018Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Results on the normality of square-free monomial ideals and cover ideals under some graph operations2021Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 127, nr 3, s. 441-457Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    Exceptional Groups and their Generators2022Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    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.

    Fulltekst (pdf)
    fulltext
  • 18.
    Alpan, Gökalp
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och partiella differentialekvationer.
    Kozhan, Rostyslav
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och partiella differentialekvationer.
    Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles2022Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 63, nr 4, artikkel-id 043505Artikkel i tidsskrift (Fagfellevurdert)
    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 torsors2020Inngår i: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-4279, Vol. 73, nr 3, s. 875-898Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Corestricted Group Actions and Eight-Dimensional Absolute Valued Algebras2012Rapport (Annet vitenskapelig)
    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.

    Fulltekst (pdf)
    fulltext
  • 21.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Morphisms in the Category of Finite Dimensional Absolute Valued Algebras2011Rapport (Annet vitenskapelig)
    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.

    Fulltekst (pdf)
    fulltext
  • 22.
    Alsaody, Seidon
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    On Finite-Dimensional Absolute Valued Algebras2012Licentiatavhandling, med artikler (Annet vitenskapelig)
    Fulltekst (pdf)
    fulltext
  • 23.
    Alsaody, Seidon
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    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)2021Inngår i: Forum of Mathematics, Sigma, ISSN 2050-5094, Vol. 9, artikkel-id e75Artikkel i tidsskrift (Fagfellevurdert)
    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).

    Fulltekst (pdf)
    FULLTEXT01
  • 24.
    Alsätra, Tova
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Knots, Reidemeister Moves and Knot Invariants2019Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 25.
    Alverbro, Miranda
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    An Overwiev Of The Rado Graph2022Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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.

    Fulltekst (pdf)
    fulltext
  • 26.
    Andersson, Anders
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    On second-order generalized quantifiers and finite structures2002Inngår i: Ann. Pure Appl. Logic, Vol. 115, nr 1-3, s. 1-32Artikkel i tidsskrift (Fagfellevurdert)
  • 27.
    Andersson, Evelina
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Random sampling of finite graphs with constraints2014Independent thesis Advanced level (degree of Master (One Year)), 20 poäng / 30 hpOppgave
    Fulltekst (pdf)
    fulltext
    Fulltekst (pdf)
    appendix
  • 28. Armstrong, Alasdair
    et al.
    Struth, Georg
    Weber, Tjark
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datalogi.
    Programming and automating mathematics in the Tarski-Kleene hierarchy2014Inngår i: Journal of Logical and Algebraic Methods in Programming, ISSN 2352-2208, Vol. 83, nr 2, s. 87-102Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Linking and Morse Theory2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 30.
    Asplund, Teo
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Extremal Hypergraphs2013Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 31.
    Awodey, Steve
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Eliasson, Jonas
    Ultrasheaves and double negation2002Rapport (Annet vitenskapelig)
  • 32. Awodey, Steve
    et al.
    Eliasson, Jonas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    Ultrasheaves and double negation2004Inngår i: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 45, nr 4, s. 235-245Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Tillämpad beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap.
    Reichel, Lothar
    Kent State Univ, Dept Math Sci, Kent, OH 44242 USA..
    Editorial: Novel methods and theories in numerical algebra with interdisciplinary applications2018Inngår i: Numerical Linear Algebra with Applications, ISSN 1070-5325, E-ISSN 1099-1506, Vol. 25, nr 4, artikkel-id e2181Artikkel i tidsskrift (Annet vitenskapelig)
  • 34.
    Bengtsson, Niclas
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    Abstract Logics and Lindström's Theorem2023Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    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.

    Fulltekst (pdf)
    fulltext
  • 35.
    Berg, Sandra
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Global dimension of (higher) Nakayama algebras2020Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 36.
    Berg, Sandra
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Om talet Π2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 37.
    Berglund, Björn
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Arkimedes metod2017Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 38.
    Bjerkeng van Keppel, Alvar
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    The Unprovability of the Continuum Hypothesis Using the Method of Forcing2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 39.
    Björklund, Johan
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Flexible isotopy classification of flexible links2016Inngår i: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 25, nr 8, artikkel-id 1650049Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Stoltenberg-Hansen, V
    Tucker, J.V.
    Domain representations of partial functions, with applications to spatial objects and contructive volume geometry2001Rapport (Annet vitenskapelig)
  • 41.
    Blanck, Jens
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Matematisk logik.
    Stoltenberg-Hansen, Viggo
    Tucker, John V.
    Domain representations of partial functions, with applications to spatial objects and constructive volume geometry2002Inngår i: Theoret. Comput. Sci., Vol. 284, nr 2, s. 207-240Artikkel i tidsskrift (Fagfellevurdert)
  • 42.
    Block, Max
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Undecidability of finite satisfiability and characterization of NP in finite model theory2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 43.
    Blomqvist, Christer
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Miniräknarmania: eller hur att få ut så mycket som möjligt från en enkel reklamräknare2014Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 44.
    Bocca, Gabriele
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Quasi-hereditary covers of higher zigzag algebras of type A2021Inngår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 225, nr 1, artikkel-id 106466Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    On the Lie algebra structure of integrable derivations2023Inngår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 55, nr 6, s. 2617-2634Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    Stable invariance of the restricted Lie algebra structure of Hochschild cohomology2022Inngår i: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 321, nr 1, s. 45-71Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
    From quasi-hereditary algebras with exact Borel subalgebras to directed bocses2020Inngår i: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 52, nr 2, s. 367-378Artikkel i tidsskrift (Fagfellevurdert)
    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 universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra, logik och representationsteori.
    Polynomial functors and two-parameter quantum symmetric pairs2023Inngår i: Transformation groups, ISSN 1083-4362, E-ISSN 1531-586X, Vol. 28, nr 1, s. 107-149Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    FULLTEXT01
  • 49.
    Bäck, Viktor
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Localization of Multiscale Screened Poisson Equation2012Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
  • 50.
    Carlbaum, Wilhelm
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Algebra och geometri.
    Primtal och kryptografi2016Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Fulltekst (pdf)
    fulltext
1234567 1 - 50 of 450
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