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Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras (Cambridge Studies in Advanced Mathematics)by D. Benson
Synopses & ReviewsPublisher Comments:Now in paperback, this is the first of two volumes that provide an introduction to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras; the author emphasizes modular representations and the homological algebra associated with their categories. This volume concentrates on the cohomology of groups, always with representations in view. Benson also gives an overview of the algebraic topology and Ktheory associated with the cohomology of groups and discusses algebraic and topological proofs of the finite generation of the cohomology ring of a finite group. The book culminates in a chapter dealing with the theory of varieties for modules. Much of the material presented here has never appeared before in book form. Consequently students and research workers studying group theory, and indeed algebra, will appreciate this exposition on the essential results of modern representation theory.
Synopsis:This volume is a selfcontained introduction to the ideas needed to understand modern developments in the representation theory of finite groups and associative algebras. Much of the material presented here has never appeared before in book form.
Synopsis:Now in paperback this is the second of two volumes that will provide an introdcution to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras; the author emphasises modular representations and the homological algebra associated with their categories.This volume concentrates on the cohomology of groups, always with representations in view.
Synopsis:This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finitedimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (AuslanderReiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almostsplit sequences are discussed in some detail.
Synopsis:Author D. Benson concentrates on the cohomology of groups, always with representations in view. He also gives an overview of the algebraic topology and Ktheory associated with the cohomology of groups and discusses algebraic and topological proofs of the finite generation of the cohomology ring of a finite group. Students and researchers will appreciate this exposition on the essential results of modern representation theory.
Description:Includes bibliographical references and indexes.
Table of Contents1. Background material from rings and modules; 2. Homological algebra; 3. Modules for group algebra; 4. Methods from the representation of algebra; 5. Representation rings and Burnside rings; 6. Block theory.
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