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Mutations of Alternative Algebras

  • Alberto Elduque
  • Hyo Chul Myung

Part of the Mathematics and Its Applications book series (MAIA, volume 278)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Alberto Elduque, Hyo Chul Myung
    Pages 1-50
  3. Alberto Elduque, Hyo Chul Myung
    Pages 51-91
  4. Alberto Elduque, Hyo Chul Myung
    Pages 92-135
  5. Alberto Elduque, Hyo Chul Myung
    Pages 136-181
  6. Alberto Elduque, Hyo Chul Myung
    Pages 182-210
  7. Back Matter
    Pages 211-226

About this book

Introduction

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.

Keywords

algebra associative algebra automorphism classical mechanics homomorphism mechanics

Authors and affiliations

  • Alberto Elduque
    • 1
  • Hyo Chul Myung
    • 2
  1. 1.Department of MathematicsUniversity of ZaragozaZaragozaSpain
  2. 2.Department of MathematicsUniversity of Northern IowaCedar FallsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8279-7
  • Copyright Information Springer Science+Business Media B.V. 1994
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4373-3
  • Online ISBN 978-94-015-8279-7
  • Buy this book on publisher's site