Alternative Algebras
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Mutations Of Alternative Algebras
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Author : Alberto Elduque
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mutations Of Alternative Algebras written by Alberto Elduque and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
An Introduction To Nonassociative Algebras
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Author : Richard Donald Schafer
language : en
Publisher: Courier Corporation
Release Date : 2017-12-13
An Introduction To Nonassociative Algebras written by Richard Donald Schafer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-13 with Mathematics categories.
"An important addition to the mathematical literature … contains very interesting results not available in other books; written in a plain and clear style, it reads very smoothly." — Bulletin of the American Mathematical Society This concise study was the first book to bring together material on the theory of nonassociative algebras, which had previously been scattered throughout the literature. It emphasizes algebras that are, for the most part, finite-dimensional over a field. Written as an introduction for graduate students and other mathematicians meeting the subject for the first time, the treatment's prerequisites include an acquaintance with the fundamentals of abstract and linear algebra. After an introductory chapter, the book explores arbitrary nonassociative algebras and alternative algebras. Subsequent chapters concentrate on Jordan algebras and power-associative algebras. Throughout, an effort has been made to present the basic ideas, techniques, and flavor of what happens when the associative law is not assumed. Many of the proofs are given in complete detail.
Alternative Algebras
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Author :
language : en
Publisher:
Release Date : 1976
Alternative Algebras written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Alternative Nucleus Of Right Alternative Algebras
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Author : Seong Nam Ng
language : en
Publisher:
Release Date : 1985
Alternative Nucleus Of Right Alternative Algebras written by Seong Nam Ng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Algebra categories.
Alternative Loop Rings
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Author : E.G. Goodaire
language : en
Publisher: Elsevier
Release Date : 1996-10-24
Alternative Loop Rings written by E.G. Goodaire and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-24 with Mathematics categories.
For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously. One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups. Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest. This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known. The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.
Alternative Algebras Over An Arbitrary Field
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Author : Richard Donald Schafer
language : en
Publisher:
Release Date : 1943
Alternative Algebras Over An Arbitrary Field written by Richard Donald Schafer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1943 with Algebra, Abstract categories.
Non Associative Algebra And Its Applications
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Author : Lev Sabinin
language : en
Publisher: CRC Press
Release Date : 2006-01-13
Non Associative Algebra And Its Applications written by Lev Sabinin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Mathematics categories.
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
Nonassociative Algebra And Its Applications
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Author : R. Costa
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Nonassociative Algebra And Its Applications written by R. Costa and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Mathematics categories.
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
Algebra And Applications 1
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Author : Abdenacer Makhlouf
language : en
Publisher: John Wiley & Sons
Release Date : 2021-03-31
Algebra And Applications 1 written by Abdenacer Makhlouf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Mathematics categories.
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
On A Generalization Of Alternative Algebras
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Author : Raymond Victor Morgan
language : en
Publisher:
Release Date : 1969
On A Generalization Of Alternative Algebras written by Raymond Victor Morgan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.