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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, 361-368 p.Article in journal (Refereed)
  • 2.
    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
  • 3.
    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, 977-995 p.Article 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.

  • 4.
    Ahlman, Ove
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    >k-homogeneous infinite graphs2017In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902Article 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.

    The full text will be freely available from 2019-09-05 16:29
  • 5.
    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, 435-456 p.Article 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.

    The full text will be freely available from 2018-02-15 15:28
  • 6.
    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)
  • 7.
    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, ISSN 1759-9008, E-ISSN 1759-9008, Vol. 7, no 2, 1-53 p., 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.

  • 8.
    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, 223-250 p.Article 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.

  • 9.
    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, 32-58 p.Article 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).

  • 10.
    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
  • 11.
    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.

  • 12.
    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.

  • 13.
    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)
  • 14.
    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, 1-32 p.Article in journal (Refereed)
  • 15.
    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
  • 16. 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, 87-102 p.Article 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. 

  • 17.
    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
  • 18.
    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
  • 19. 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, Vol. 45, no 4, 235-245 p.Article 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.

  • 20.
    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)
  • 21.
    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
  • 22.
    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
  • 23.
    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
  • 24.
    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, 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.

  • 25.
    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)
  • 26.
    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, 207-240 p.Article in journal (Refereed)
  • 27.
    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
  • 28.
    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
  • 29.
    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
  • 30.
    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
  • 31. Coquand, Thiery
    et al.
    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.
    Metric boolean algebras and constructive measure theory2002In: Arch. Math. Logic, Vol. 41, 687-704 p.Article in journal (Refereed)
  • 32.
    Coulembier, Kevin
    et al.
    Univ Ghent, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Primitive ideals, twisting functors and star actions for classical Lie superalgebras2016In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 718, 207-253 p.Article in journal (Refereed)
    Abstract [en]

    We study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov's twisting functors on the BGG category O. The third topic addresses deformed orbits of the Weyl group. These take over the role of the usual Weyl group orbits for Lie algebras, in the study of primitive ideals and twisting functors for Lie superalgebras.

  • 33.
    Courte, Sylvain
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Legendrian submanifolds with Hamiltonian isotopic symplectizations2016In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 16, no 6, 3641-3652 p.Article in journal (Refereed)
    Abstract [en]

    In any closed contact manifold of dimension at least 1 1, we construct examples of closed Legendrian submanifolds which are not diffeomorphic but whose Lagrangian cylinders in the symplectization are Hamiltonian isotopic.

  • 34.
    Crispin Quiñonez, Veronica
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Minimal reductions of monomial ideals in dimension two2016Report (Refereed)
  • 35.
    Dahlgren, Fredrik
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Effective Distribution Theory2007Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we introduce and study a notion of effectivity (or computability) for test functions and for distributions. This is done using the theory of effective (Scott-Ershov) domains and effective domain representations.

    To be able to construct effective domain representations of the spaces of test functions considered in distribution theory we need to develop the theory of admissible domain representations over countable pseudobases. This is done in the first paper of the thesis. To construct an effective domain representation of the space of distributions, we introduce and develop a notion of partial continuous function on domains. This is done in the second paper of the thesis. In the third paper we apply the results from the first two papers to develop an effective theory of distributions using effective domains. We prove that the vector space operations on each space, as well as the standard embeddings into the space of distributions effectivise. We also prove that the Fourier transform (as well as its inverse) on the space of tempered distributions is effective. Finally, we show how to use convolution to compute primitives on the space of distributions. In the last paper we investigate the effective properties of a structure theorem for the space of distributions with compact support. We show that each of the four characterisations of the class of compactly supported distributions in the structure theorem gives rise to an effective domain representation of the space. We then use effective reductions (and Turing-reductions) to study the reducibility properties of these four representations. We prove that three of the four representations are effectively equivalent, and furthermore, that all four representations are Turing-equivalent. Finally, we consider a similar structure theorem for the space of distributions supported at 0.

    List of papers
    1. Admissible Domain Representations of Inductive Limit Spaces
    Open this publication in new window or tab >>Admissible Domain Representations of Inductive Limit Spaces
    In: Mathematical Structures in Computer ScienceArticle in journal (Refereed) Submitted
    Identifiers
    urn:nbn:se:uu:diva-96205 (URN)
    Available from: 2007-09-21 Created: 2007-09-21Bibliographically approved
    2. Partial Continuous Functions and Admissible Domain Representations
    Open this publication in new window or tab >>Partial Continuous Functions and Admissible Domain Representations
    2007 (English)In: Journal of logic and computation (Print), ISSN 0955-792X, E-ISSN 1465-363X, Vol. 17, no 6, 1063-1081 p.Article in journal (Refereed) Published
    Abstract [en]

    It is well known that to be able to represent continuous functions between domain representable spaces it is critical that the domain representations of the spaces we consider are dense. In this article we show how to develop a representation theory over a category of domains with morphisms partial continuous functions. The raison detre for introducing partial continuous functions is that by passing to partial maps, we are free to consider totalities which are not dense. We show that the category of admissibly representable spaces with morphisms functions which are representable by it partial continuous function is Cartesian closed. Finally, we consider the question of effectivity.

    National Category
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-96206 (URN)10.1093/logcom/exm034 (DOI)000252665100004 ()
    Available from: 2007-09-21 Created: 2007-09-21 Last updated: 2011-03-24Bibliographically approved
    3. A Domain Theoretic Approach to Effective Distribution Theory
    Open this publication in new window or tab >>A Domain Theoretic Approach to Effective Distribution Theory
    Manuscript (Other academic)
    Identifiers
    urn:nbn:se:uu:diva-96207 (URN)
    Available from: 2007-09-21 Created: 2007-09-21 Last updated: 2010-01-13Bibliographically approved
    4. Effective Structure Theorems for Spaces of Compactly Supported Distributions
    Open this publication in new window or tab >>Effective Structure Theorems for Spaces of Compactly Supported Distributions
    Manuscript (Other academic)
    Identifiers
    urn:nbn:se:uu:diva-96208 (URN)
    Available from: 2007-09-21 Created: 2007-09-21 Last updated: 2010-01-13Bibliographically approved
  • 36.
    Dahlgren, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Logic.
    Partial continuous functions and admissible domain representations: Extended abstract2006In: Logical approaches to computational barriers: Proceedings / [ed] Beckmann A; Berger U; Lowe B; Tucker JV, 2006, Vol. 3988, 94-104 p.Conference paper (Refereed)
    Abstract [en]

    It is well known that to be able to represent continuous functions between domain representable spaces it is critical that the domain representations of the spaces we consider are dense. In this article we show how to develop a representation theory over a category of domains with morphisms partial continuous functions. The reason for introducing partial continuous functions is that by passing to partial maps, we are free to consider totalities which are not dense. We show that there is a natural subcategory of the category of representable spaces with morphisms representable maps which is Cartesian closed. Finally, we consider the question of effectivity.

  • 37.
    Darpö, Erik
    et al.
    University of Oxford.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    The double sign of a real division algebra of finite dimension greater than one2011Report (Other academic)
    Abstract [en]

    For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a E A \ {0} are shown to form an invariant of A, called its double sign. For each n E {2, 4, 8}, the double sign causes the category Dn of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of Dn.

  • 38. Darpö, Erik
    et al.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    The double sign of a real division algebra of finite dimension greater than one2012In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 285, no 13, 1635-1642 p.Article in journal (Refereed)
    Abstract [en]

    For any real division algebra A of finite dimension greater than one, the signs of the determinants of left multiplication and right multiplication by an element a is an element of A\{0} are shown to form an invariant of A, called its double sign. For each n is an element of {2, 4, 8}, the double sign causes the category D-n of all n-dimensional real division algebras to decompose into four blocks. The structures of these blocks are closely related, and their relationship is made precise for a sample of full subcategories of D-n.

  • 39.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    A general approach to finite dimensional division algebras2011Report (Other academic)
    Abstract [en]

    We present a short and rather self-contained introduction to the theory of finite dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories Dn(k), and the role played by the irreducible morphisms. Sections 4-5 deal with the classical case of real division algebras, emphasizing the double sign decomposition of the level subcategories Dn(R) for n E {2, 4, 8} and the problem of describing their blocks, along with an account of known partial solutions to this problem.

  • 40.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    A general approach to finite dimensional division algebras2012In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 126, no 1, 73-86 p.Article in journal (Refereed)
    Abstract [en]

    We present a short and rather self-contained introduction to the theory of finite-dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In Sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories D-n(k), and the role played by the irreducible morphisms. Sections 4-5 deal with the classical case of real division algebras, emphasizing the double sign decomposition of the level subcategories D-n(R) for n is an element of {2, 4, 8} and the problem of describing their blocks, along with an account of known partial solutions to this problem. 

  • 41.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Construction of Auslander-Reiten quivers for a class of group rings1983In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 183, no 1, 43-60 p.Article in journal (Refereed)
  • 42.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Dissident algebras1999In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 82, no 1, 13-23 p.Article in journal (Refereed)
  • 43.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Fraleighs misstag: en varning2000In: Normat, Vol. 48, 153-158 p.Article in journal (Refereed)
  • 44.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Group rings of wild representation type1983In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 266, no 1, 1-22 p.Article in journal (Refereed)
  • 45.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Lattices over curve singularities with large conductor1993In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 114, no 1, 399-433 p.Article in journal (Refereed)
  • 46.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Lattices over group rings of cyclic p-groups and generalized factorspace categories1985In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. s2-31, no 3, 407-424 p.Article in journal (Refereed)
  • 47.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Power-associative real division algebras1998In: Canadian Mathematical Society Conference Proceedings, Vol. 24, 139-144 p.Article in journal (Refereed)
  • 48.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Quadratic division algebras revisited. (Remarks on an article by J. M. Osborn.)2000In: Proceedings of the American Mathematical Society, Vol. 128, 3159-3166 p.Article in journal (Refereed)
  • 49.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Reduction of isolated singularities1987In: Commentarii Mathematici Helvetici, ISSN 0010-2571, E-ISSN 1420-8946, Vol. 62, no 1, 654-676 p.Article in journal (Refereed)
  • 50.
    Dieterich, Ernst
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Representation types of group rings over complete discrete valuation rings1981In: Lecture notes in mathematics, ISSN 0075-8434, Vol. 882, 369-389 p.Article in journal (Refereed)
12345 1 - 50 of 244
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