Modules and Group Algebras

Overview

These notes grew out of a Nachdiplom course given at the ETH Zurich in the summer semester of 1995. They aim at the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. The book presents an entirely new approach to the subject based on the recent development in this field. Basically the shift has been towards a much more categorical view of representation theory, and an expansion of the viewpoint to include ...
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Paperback (1996)
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Overview

These notes grew out of a Nachdiplom course given at the ETH Zurich in the summer semester of 1995. They aim at the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. The book presents an entirely new approach to the subject based on the recent development in this field. Basically the shift has been towards a much more categorical view of representation theory, and an expansion of the viewpoint to include infinitely generated modules as well as the finitely generated ones. Some of the constructions in the category of all modules have had new and original applications for the category of finitely generated modules. This introduction to a fresh view of the module theory for finite groups is of interest to students and researchers in homotopy theory and group actions as well as the representation theory of finite groups.
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Editorial Reviews

Booknews
An introduction to the interaction of homological algebra, the cohomology of groups, and modular representation theory. The volume presents a new approach based on the shift towards a more categorical view of representation theory, and an expansion to include infinitely generated modules as well as finitely generated ones. The organization of the subjects was based on a Nachdiplom course given at the ETH Zurich in 1995. Includes illustrations and equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

1 Augmentations, nilpotent ideals, and semisimplicity.- 2 Tensor products, Homs, and duality.- 3 Restriction and induction.- 4 Projective resolutions and cohomology.- 5 The stable category.- 6 Products in cohomology.- 7 Examples and diagrams.- 8 Relative projectivity.- 9 Relative projectivity and ideals in cohomology.- 10 Varieties and modules.- 11 Infinitely generated modules.- 12 Idempotent modules.- 13 Varieties and induced modules.- References.- List of symbols.

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