Alternative Algebras Over An Arbitrary Field
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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.
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.
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.
Albert Algebras Over Commutative Rings
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Author : Skip Garibaldi
language : en
Publisher: Cambridge University Press
Release Date : 2024-10-31
Albert Algebras Over Commutative Rings written by Skip Garibaldi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Mathematics categories.
Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering results in characteristic 2 and 3, many results are proven for Albert algebras over an arbitrary commutative ring, showing that they hold in this greater generality. The book extensively covers requisite knowledge, such as non-associative algebras over commutative rings, scalar extensions, projective modules, alternative algebras, and composition algebras over commutative rings, with a special focus on octonion algebras. It then goes into Jordan algebras, Lie algebras, and group schemes, providing exercises so readers can apply concepts. This centralized resource illuminates the interplay between results that use only the structure of Albert algebras and those that employ theorems about group schemes, and is ideal for mathematics and physics researchers.
Non Unital Composition Algebras
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Author : Hyo Chul Myung
language : en
Publisher:
Release Date : 1994
Non Unital Composition Algebras written by Hyo Chul Myung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebra 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.
The Book Of Involutions
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Author : Max-Albert Knus
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
The Book Of Involutions written by Max-Albert Knus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Written for graduate students and research mathematicians, this monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. Involutions are viewed as twisted forms of hermitian quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are discussed, as well as: groups of type F4 or G2 arising from exceptional Jordan or composition algebras, the discriminant algebra of an algebra with unitary involution, and the algebra-theoretic counterpart to linear groups of type D4. Annotation copyrighted by Book News, Inc., Portland, OR.
Second International Conference On Algebra
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Author : Leonid Arkadʹevich Bokutʹ
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Second International Conference On Algebra written by Leonid Arkadʹevich Bokutʹ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honour of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.
An Introduction To Nonassociative Algebras
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Author : Richard D. Schafer
language : en
Publisher: Courier Dover Publications
Release Date : 2017-11-15
An Introduction To Nonassociative Algebras written by Richard D. Schafer and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
Concise graduate-level introductory study presents some of the important ideas and results in the theory of nonassociative algebras. Places particular emphasis on alternative and (commutative) Jordan algebras. 1966 edition.
Malcev Admissible Algebras
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Author : H.C. Myung
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Malcev Admissible Algebras written by H.C. Myung 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 2013-11-21 with Science categories.