Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras
Title Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras PDF eBook
Author D. J. Benson
Publisher Cambridge University Press
Pages 260
Release 1998-06-18
Genre Mathematics
ISBN 9780521636537

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An introduction to modern developments in the representation theory of finite groups and associative algebras.

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules
Title Representations and Cohomology: Volume 2, Cohomology of Groups and Modules PDF eBook
Author D. J. Benson
Publisher Cambridge University Press
Pages 296
Release 1991-08-22
Genre Mathematics
ISBN 9780521636520

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A further introduction to modern developments in the representation theory of finite groups and associative algebras.

Representations and Cohomology

Representations and Cohomology
Title Representations and Cohomology PDF eBook
Author David J. Benson
Publisher
Pages 279
Release 1991
Genre Homology theory
ISBN

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Representation Theory

Representation Theory
Title Representation Theory PDF eBook
Author Alexander Zimmermann
Publisher Springer
Pages 720
Release 2014-08-15
Genre Mathematics
ISBN 3319079689

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Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

Introduction to Representation Theory

Introduction to Representation Theory
Title Introduction to Representation Theory PDF eBook
Author Pavel I. Etingof
Publisher American Mathematical Soc.
Pages 240
Release 2011
Genre Mathematics
ISBN 0821853511

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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.

Elements of the Representation Theory of Associative Algebras: Volume 1

Elements of the Representation Theory of Associative Algebras: Volume 1
Title Elements of the Representation Theory of Associative Algebras: Volume 1 PDF eBook
Author Ibrahim Assem
Publisher Cambridge University Press
Pages 34
Release 2006-02-13
Genre Mathematics
ISBN 1139443186

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This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.

Representations of Algebraic Groups

Representations of Algebraic Groups
Title Representations of Algebraic Groups PDF eBook
Author Jens Carsten Jantzen
Publisher American Mathematical Soc.
Pages 594
Release 2003
Genre Mathematics
ISBN 082184377X

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Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.