Mutations of Alternative Algebras / by Alberto Elduque, Hyo Chul Myung
(Mathematics and Its Applications ; 278)
| データ種別 | 電子ブック |
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| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1994 |
| 本文言語 | 英語 |
| 大きさ | XIV, 226 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | *Elduque, Alberto author Myung, Hyo Chul author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Associative rings LCSH:Rings (Algebra) LCSH:Matrix theory LCSH:Algebra LCSH:Nonassociative rings LCSH:Physics LCSH:Mechanics FREE:Mathematics FREE:Non-associative Rings and Algebras FREE:Associative Rings and Algebras FREE:Theoretical, Mathematical and Computational Physics FREE:Linear and Multilinear Algebras, Matrix Theory FREE:Mechanics |
| 分 類 | DC23:512.48 |
| 巻冊次 | ISBN:9789401582797 
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| ISBN | 9789401582797 |
| URL | http://dx.doi.org/10.1007/978-94-015-8279-7 |
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