Modules and Group Algebras

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Springer Science & Business Media, Feb 29, 1996 - Mathematics - 92 pages
The notes in this volume were written as a part of a Nachdiplom course that I gave at the ETH in the summer semester of 1995. The aim of my lectures was the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. Every time that I had given such a course in the past fifteen years, the choice of the material and the order of presentation of the results have followed more or less the same basic pattern. Such a course began with the fundamentals of group cohomology, and then investigated the structure of cohomology rings, and their maximal ideal spectra. Then the variety of a module was defined and related to actual module structure through the rank variety. Applications followed. The standard approach was used in my University of Essen Lecture Notes [e1] in 1984. Evens [E] and Benson [B2] have written it up in much clearer detail and included it as part of their books on the subject.
 

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Contents

Augmentations nilpotent ideals and semisimplicity
2
Tensor products Homs and duality
5
Restriction and induction
9
Projective resolutions and cohomology
12
The stable category
17
Products in cohomology
26
Examples and diagrams
42
Relative projectivity
53
Varieties and modules
64
Infinitely generated modules
68
Idempotent modules
72
Varieties and induced modules
79
References
85
List of symbols
87
Index
89
Copyright

Relative projectivity and ideals in cohomology
58

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