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1. 1. Simple Modules over Lie Algebras

   Författare :Jonathan Nilsson; Volodymyr Mazorchuk; Erhard Neher; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lie algebra; Representation; Simple module; Non-weight module; Classification; Construction; Mathematics; Matematik;

   Sammanfattning : Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. LÄS MER

3. 2. A Natural Interpretation of Classical Proofs

   Författare :Jens Brage; Per Martin-Löf; Sara Negri; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Brouwer-Heyting-Kolmogorov; classical logic; constructive type theory; constructive semantics; proof interpretation; double-negation; continuation-passing-style; natural deduction; sequent calculus; cut elimination; explicit substitution; Mathematical logic; Matematisk logik;

   Sammanfattning : In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. LÄS MER

4. 3. On properties of monomial ideals and algebras

   Författare :Oleksandra Gasanova; Veronica Crispin Quiñonez; Volkmar Welker; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : Monomial ideals form an important link between commutative algebra and combinatorics. Our aim is to study various operations on monomial ideals and algebras, as well as their properties. This thesis consists of an introduction and four research articles. The introduction covers the necessary background and the existing results. LÄS MER

5. 4. Configuration spaces, props and wheel-free deformation quantization

   Författare :Theo Backman; Sergei Merkulov; Sergei Shadrin; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; operad; properad; prop; deformation quantization; configuration space; Lie bialgebra; Poisson manifold; Mathematics; matematik;

   Sammanfattning : The main theme of this thesis is higher algebraic structures that come from operads and props.The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results. LÄS MER

7. 5. A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory

   Författare :Menno de Boer; Peter LeFanu Lumsdaine; Alexander Berglund; Bas Spitters; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Dependent type theory; Category theory; Contextual categories; Initiality; Formalization; Mathematics; matematik; matematisk logik; Mathematical Logic;

   Sammanfattning : In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with 0, 1, N, A+B, ∏AB, ∑AB, IdA(u,v), countable hierarchy of universes (Ui)iєN closed under these type constructors and with type of elements (ELi(a))iєN. We employ the categorical semantics of contextual categories. LÄS MER