Sökning: "algebraic group"

Visar resultat 1 - 5 av 46 avhandlingar innehållade orden algebraic group.

1. 1. Canonical Bases for Algebraic Computations

   Författare :Patrik Nordbeck; Algebra; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; gruppteori; algebra; algebraisk geometri; fältteori; Talteori; group theory; algebraic geometry; field theory; Matematik; Number Theory; regular languages; Mathematics; composition of polynomials; factor algebras; Gröbner bases; SAGBI bases;

   Sammanfattning : This thesis deals with computational methods in algebra, mainly focusing on the concept of Gröbner and SAGBI bases in non-commutative algebras. The material has a natural division into two parts. The first part is a rather extensive treatment of the basic theory of Gröbner bases and SAGBI bases in the non-commutative polynomial ring. LÄS MER

3. 2. A Categorical Study of Composition Algebras via Group Actions and Triality

   Författare :Seidon Alsaody; Ernst Dieterich; Ryszard Rubinsztein; Alberto Elduque; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Composition algebra; division algebra; absolute valued algebra; triality; groupoid; group action; algebraic group; Lie algebra of derivations; classification.; Mathematics; Matematik;

   Sammanfattning : A composition algebra is a non-zero algebra endowed with a strictly non-degenerate, multiplicative quadratic form. Finite-dimensional composition algebras exist only in dimension 1, 2, 4 and 8 and are in general not associative or unital. Over the real numbers, such algebras are division algebras if and only if they are absolute valued, i.e. LÄS MER

4. 3. Topics in Computational Algebraic Geometry and Deformation Quantization

   Författare :Christine Jost; Sandra Di Rocco; Boris Shapiro; Gregory G. Smith; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Segre classes; Chern-Schwartz-MacPherson classes; topological Euler characteristic; computational algebraic geometry; numerical algebraic geometry; numerical homotopy methods; deformation quantization; polyvector fields; Fedosov quantization; Grothendieck-Teichmüller group; Mathematics; matematik;

   Sammanfattning : This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. LÄS MER

5. 4. Multivariable Orthogonal Polynomials as Coupling Coefficients for Lie and Quantum Algebra Representations

   Författare :Hjalmar Rosengren; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; higher order Hankel form; Wigner symbol; quadratic algebra; Clebsch-Gordan coefficient; quantum group; Lie group; highest weight representation; multivariable orthogonal and biorthogonal polynomials; multivariable hypergeometric and basic hypergeometric functions; algebraisk topologi; Geometry; Geometri; algebraic topology;

   Sammanfattning : The main topic of the thesis is the connection between representation theory and special functions. We study matrix elements, coupling coefficient, and recoupling coefficients for the simplest Lie and quantum groups. LÄS MER

7. 5. Quasi-Lie Algebras and Quasi-Deformations. Algebraic Structures Associated with Twisted Derivations

   Författare :Daniel Larsson; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Talteori; fältteori; algebraisk geometri; algebra; gruppteori; Lie Algebras; Quasi-Deformations; Number Theory; field theory; algebraic geometry; group theory; Quasi-Lie Algebras;

   Sammanfattning : This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasi-deformations? to clearly distinguish it from the classical Grothendieck-Schlessinger and Gers-tenhaber deformation schemes. The main difference is that quasi-deformations are not in gene-ral category-preserving, i.e. LÄS MER