Representation Theory of Finite Groups and Associative Algebras
Author: Charles W. Curtis
Publisher: American Mathematical Soc.
Published: 1966
Total Pages: 722
ISBN-13: 9780821869451
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Representation Theory of Finite Groups and Associative Algebras
Author: Charles W. Curtis
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 714
ISBN-13: 0821840665
DOWNLOAD EBOOK →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.
Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras
Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1998-06-18
Total Pages: 260
ISBN-13: 9780521636537
DOWNLOAD EBOOK →An introduction to modern developments in the representation theory of finite groups and associative algebras.
Methods of Representation Theory
Author: Charles W. Curtis
Publisher: Wiley-Interscience
Published: 1981
Total Pages: 984
ISBN-13:
DOWNLOAD EBOOK →Revised and expanded, this second volume presents a modern treatment of finite groups and orders. It covers classical, modular and integral representation theory and contains many important new results. Beginning with an introductory review of ring theory, algebraic number theory, and homological algebra, the book then moves on to other topics such as modular representations and integral representation theory. Also covered are class groups and Picard groups, the theory of blocks, rationality questions, indecomposable modules and more.
Representations and Cohomology: Volume 2, Cohomology of Groups and Modules
Author: D. J. Benson
Publisher: Cambridge University Press
Published: 1991-08-22
Total Pages: 296
ISBN-13: 9780521636520
DOWNLOAD EBOOK →A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Representation Theory of Finite Groups
Author: Benjamin Steinberg
Publisher: Springer Science & Business Media
Published: 2011-10-23
Total Pages: 166
ISBN-13: 1461407761
DOWNLOAD EBOOK →This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Elements of the Representation Theory of Associative Algebras: Volume 1
Author: Ibrahim Assem
Publisher: Cambridge University Press
Published: 2006-02-13
Total Pages: 480
ISBN-13: 9780521584234
DOWNLOAD EBOOK →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.
Introduction to Representation Theory
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 240
ISBN-13: 0821853511
DOWNLOAD EBOOK →Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
A Course in Finite Group Representation Theory
Author: Peter Webb
Publisher: Cambridge University Press
Published: 2016-08-19
Total Pages: 339
ISBN-13: 1107162394
DOWNLOAD EBOOK →This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Algebras and Representation Theory
Author: Karin Erdmann
Publisher: Springer
Published: 2018-09-07
Total Pages: 304
ISBN-13: 3319919989
DOWNLOAD EBOOK →This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
