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Mutations of Alternative Algebras : Mathematics and Its Applications - Alberto Elduque

Mutations of Alternative Algebras

Mathematics and Its Applications

Hardcover Published: 31st March 1994
ISBN: 9780792327356
Number Of Pages: 226

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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 alternative algebras, which are a natural generalization of mutations of associative algebras. A complete structure theory, including automorphisms, derivations and certain representations, is given for mutations of artinian alternative algebras, and, in particular, of Cayley--Dickson algebras. 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 important interplay with the theory of noncommutative (associative) algebras through mutation parameters. New simple algebras and open problems presented in this book will stimulate additional research and applications in the area.
This book will be valuable to graduate students, mathematicians and physicists interested in applications of algebras.

Nonassociative Algebrasp. 1
Definitions and basic resultsp. 2
Simple and central simple algebrasp. 9
Alternative algebrasp. 13
Malcev-admissible algebrasp. 21
Jordan-admissible algebrasp. 40
Mutations of Associative Algebrasp. 51
Identities in mutation algebrasp. 58
Simple and prime mutation algebrasp. 66
Mutations of simple associative algebrasp. 76
Radicals of mutation algebrasp. 85
Mutations of Alternative Algebrasp. 92
Basic resultsp. 96
Identitiesp. 103
Mutations of Cayley-Dickson algebrasp. 109
Simple and prime mutations of alternative algebrasp. 125
Mutations of artinian alternative algebrasp. 130
Automorphisms and Derivationsp. 136
Jordan homomorphisms and derivationsp. 142
Automorphisms of mutations of associative algebrasp. 147
Derivations of mutations of associative algebrasp. 159
Composition algebras: The associative casep. 163
Composition algebras: The octonion casep. 173
The Mutation Variety and Strict Representationsp. 182
Basic conceptsp. 183
Identities for the mutation varietyp. 187
Additional properties of the mutation varietyp. 198
Strict representations of mutation algebrasp. 201
Referencesp. 211
Symbol Indexp. 219
Subject Indexp. 223
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792327356
ISBN-10: 0792327357
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 226
Published: 31st March 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.28 x 16.41  x 1.93
Weight (kg): 0.53

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