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Mutations of Alternative Algebras

Author: Alberto Elduque; Hyo Chul Myung
Publisher: Dordrecht : Springer Netherlands, 1994.
Series: Mathematics and Its Applications, 278.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Around 1978, a mutation of associative algebras was introduced to generalize the formalism of classical mechanics as well as quantum mechanics. This volume presents the first book devoted to a self-contained and detailed treatment of the mathematical theory of mutation algebras, which is based on research in this subject over the past fifteen years. The book also deals with a broader class of algebras, mutations of  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Alberto Elduque; Hyo Chul Myung
ISBN: 9789401582797 9401582793
OCLC Number: 851387511
Description: 1 online resource (xiii, 226 pages).
Contents: I Nonassociative Algebras --
1. Definitions and basic results --
2. Simple and central simple algebras --
3. Alternative algebras --
4. Malcev-admissible algebras --
5. Jordan-admissible algebras --
II Mutations of Associative Algebras --
1. Introduction --
2. Identities in mutation algebras --
3. Simple and prime mutation algebras --
4. Mutations of simple associative algebras --
5. Radicals of mutation algebras --
III Mutations of Alternative Algebras --
1. Introduction --
2. Basic results --
3. Identities --
4. Mutations of Cayley-Dickson algebras --
5. Simple and prime mutations of alternative algebras --
6. Mutations of artinian alternative algebras --
IV Automorphisms and Derivations --
1. Introduction --
2. Jordan homomorphisms and derivations --
3. Automorphisms of mutations of associative algebras --
4. Derivations of mutations of associative algebras --
5. Composition algebras: The associative case --
6. Composition algebras: The octonion case --
V The Mutation Variety and Strict Representations --
1. Basic concepts --
2. Identities for the mutation variety --
3. Additional properties of the mutation variety --
4. Strict representations of mutation algebras --
References --
Symbol Index.
Series Title: Mathematics and Its Applications, 278.
Responsibility: by Alberto Elduque, Hyo Chul Myung.

Abstract:

Since the mutation algebras do not form a variety, the structure theory explored in this volume takes quite a different approach from the standard theory of nonassociative algebras and provides an  Read more...

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