Search for dissertations about: "Affine Lie algebras"

Showing result 1 - 5 of 7 swedish dissertations containing the words Affine Lie algebras.

2. 1. Irreducible Representations of Quantum Affine Algebras

   Author : Jesper Thorén; Matematik (naturvetenskapliga fakulteten); []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Number Theory; Matematik; Mathematics; quantum evaluation modules; highest weight representations; quantum Yang-Baxter equation; quantum affine algebras; quantum groups; comultiplication; Hopf algebras; affine Lie algebras; field theory; algebraic geometry; algebra; group theory; Talteori; fältteori; algebraisk geometri; gruppteori;

   Abstract : We construct finite-dimensional representations of the quantum affine algebra associated to the simple finite-dimensional Lie algebra sl(n+1). The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. READ MORE

4. 2. Dualities, affine vertex operator algebras, and geometry of complex polynomials

   Author : Julius Borcea; Matematik (naturvetenskapliga fakulteten); []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Sendov s conjecture; annihilating fields; relative vertex operators; twisted modules; vertex operator algebras; Affine Lie algebras; standard modules; geometry of polynomials.; Mathematics; Matematik;

   Abstract : This thesis consists of two parts which deal with different subjects. In the first part we study certain aspects of the representation theory of affine Kac-Moody Lie algebras and related structures. READ MORE

5. 3. Low-dimensional cohomology of current Lie algebras

   Author : Pasha Zusmanovich; Rikard Bögvad; Dimitry Leites; Semyon Konstein; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Current Lie algebra; modular Lie algebra; Kac-Moody algebra; cohomology; Algebra; geometry and mathematical analysis; Algebra; geometri och analys; matematik; Mathematics;

   Abstract : We deal with low-dimensional homology and cohomology of current Lie algebras, i.e., Lie algebras which are tensor products of a Lie algebra L and an associative commutative algebra A. READ MORE

6. 4. Computational algorithms for algebras

   Author : Samuel Lundqvist; Clas Löfwall; Ralf Fröberg; H. Michael Möller; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Hilbert function; Gröbner basis; zero-dimensional ideal; affine variety; projective variety; run-time complexity; Algebra and geometry; Algebra och geometri; Mathematics; matematik;

   Abstract : This thesis consists of six papers. In Paper I, we give an algorithm for merging sorted lists of monomials and together with a projection technique, we obtain a new complexity bound for the Buchberger-Möller algorithm and the FGLM algorithm. READ MORE

7. 5. On Vertex Operator Algebras of Affine Type at Admissible Levels

   Author : Thomas Edlund; Matematik (naturvetenskapliga fakulteten); []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Vertex operator algebras; Kac-Moody algebras; Ore localization; Admissible levels; Singular vectors; Intertwining operators;

   Abstract : The main purpose of this thesis is the study of the structure and representation theory of simple vertex operator algebras (VOAs) of affine type at admissible levels. To do this, it is crucial to obtain knowledge of the singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. READ MORE