Sökning: "Composition algebras"

Visar resultat 1 - 5 av 8 avhandlingar innehållade orden Composition algebras.

1. 1. Kantor Triple Systems

   Författare :Daniel Mondoc; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; gruppteori; fältteori; algebra; algebraic geometry; group theory; Talteori; field theory; Number Theory; Composition algebras; Jordan algebras; Kantor triple systems; Lie algebras; Jordan triple systems; algebraisk geometri;

   Sammanfattning : The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of K-simple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. 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. Problems in the Classification Theory of Non-Associative Simple Algebras

   Författare :Erik Darpö; Ernst Dieterich; Karl-Heinz Fieseler; William Crawley-Boevey; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Division algebra; flexible algebra; normal form; composition algebra; absolute valued algebra; vector product; rotation.; MATHEMATICS; MATEMATIK;

   Sammanfattning : In spite of its 150 years history, the problem of classifying all finite-dimensional division algebras over a field k is still unsolved whenever k is not algebraically closed. The present thesis concerns some different aspects of this problem, and the related problems of classifying all composition and absolute valued algebras. LÄS MER

5. 4. 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

7. 5. Dynamical Systems and Commutants in Non-Commutative Algebras

   Författare :Alex Behakanira Tumwesigye; Sergei Silvestrov; Johan Richter; Linus Carlsson; Olga Liivapuu; Mälardalens högskola; []
   Nyckelord :Mathematics Applied Mathematics; matematik tillämpad matematik;

   Sammanfattning : This thesis work is about commutativity which is a very important topic in Mathematics, Physics, Engineering and many other fields. In Mathematics, it is well known that matrix multiplication (or composition of linear operators on a finite dimensional vector space) is not always commutative. LÄS MER