Mutations of Alternative Algebras
By: by Alberto Elduque, Hyo Chul Myung
Contributors: Myung, Hyo Chul
Series: Mathematics and Its Applications -- 278; Mathematics and Its Applications -- 278
Publisher: Springer Netherlands
Published: 1994
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 226
ISBN-13: 9789048143733; 9789401582797
Subjects: Mechanics; Mathematics; Algebra; Matrix theory
Description: 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.
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