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: 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.

Modular Representation Theory

Modular Representation Theory
Title Modular Representation Theory PDF eBook
Author D. Benson
Publisher Springer Science & Business Media
Pages 246
Release 1984
Genre Mathematics
ISBN 3540133895

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This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.

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.

Cohomology of Groups

Cohomology of Groups
Title Cohomology of Groups PDF eBook
Author Kenneth S. Brown
Publisher Springer Science & Business Media
Pages 318
Release 2012-12-06
Genre Mathematics
ISBN 1468493272

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Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.

Modular Forms and Galois Cohomology

Modular Forms and Galois Cohomology
Title Modular Forms and Galois Cohomology PDF eBook
Author Haruzo Hida
Publisher Cambridge University Press
Pages 358
Release 2000-06-29
Genre Mathematics
ISBN 9780521770361

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Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

Local Representation Theory

Local Representation Theory
Title Local Representation Theory PDF eBook
Author J. L. Alperin
Publisher Cambridge University Press
Pages 198
Release 1993-09-24
Genre Mathematics
ISBN 9780521449267

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The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.