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Author: R.S. Pierce
Publisher: Springer Science & Business Media
ISBN: 1475701632
Category : Mathematics
Languages : en
Pages : 448
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Book Description
For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con tributes to and draws from such topics as group theory, commutative ring theory, field theory, algebraic number theory, algebraic geometry, homo logical algebra, and category theory. It even has some ties with parts of applied mathematics.
Author: R.S. Pierce
Publisher: Springer Science & Business Media
ISBN: 1475701632
Category : Mathematics
Languages : en
Pages : 448
Get Book
Book Description
For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con tributes to and draws from such topics as group theory, commutative ring theory, field theory, algebraic number theory, algebraic geometry, homo logical algebra, and category theory. It even has some ties with parts of applied mathematics.
Author: Mercedes Siles Molina
Publisher: Springer Nature
ISBN: 3030352560
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.
Author: Charles W. Curtis
Publisher: American Mathematical Soc.
ISBN: 0821840665
Category : Mathematics
Languages : en
Pages : 714
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Book Description
Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
Author: Susumu Okubo
Publisher: Cambridge University Press
ISBN: 0521472156
Category : Mathematics
Languages : en
Pages : 152
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Book Description
In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and YangSHBaxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works.
Author: Richard D. Schafer
Publisher: Courier Dover Publications
ISBN: 0486164179
Category : Mathematics
Languages : en
Pages : 176
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Book Description
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.
Author: Ibrahim Assem
Publisher: Cambridge University Press
ISBN: 9780521584234
Category : Mathematics
Languages : en
Pages : 480
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Book Description
This is the first of a two-volume set that provides a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. The treatment is self-contained and provides an elementary and up-to-date introduction to the subject using quiver-theoretical techniques and the theory of almost split sequences as well as tilting theory and the use of integral quadratic forms. Much of this material has never appeared before in book form. The book is primarily addressed to graduate students starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the ten chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study. Book jacket.
Author: Abraham Adrian Albert
Publisher: American Mathematical Soc.
ISBN: 9780821870556
Category : Associative algebras
Languages : en
Pages : 824
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Book Description
This book contains the collected works of A. Adrian Albert, a leading algebraist of the twentieth century. Albert made many important contributions to the theory of the Brauer group and central simple algeras, Riemann matrices, nonassociative algebras and other topics. Part 1 focuses on associative algebras and Riemann matrices part 2 on nonassociative algebras and miscellany. Because much of Albert's work remains of vital interest in contemporary research, this volume will interst mathematicians in a variety of areas.
Author: Alexander Abian
Publisher: Elsevier
ISBN: 1483186792
Category : Mathematics
Languages : en
Pages : 175
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Book Description
Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems. The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras. The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.
Author: Charles W. Curtis
Publisher: American Mathematical Soc.
ISBN: 9780821869451
Category : Mathematics
Languages : en
Pages : 722
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Book Description
Author: Helena Albuquerque
Publisher: Springer Nature
ISBN: 3031327071
Category : Mathematics
Languages : en
Pages : 305
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Book Description
This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.
