Sökning: "Division algebra"

Hittade 3 avhandlingar innehållade orden Division algebra.

  1. 1. 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

  3. 2. 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

  4. 3. 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