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Modules and Group Algebras

  • Book
  • © 1996

Overview

Authors:
  1. Jon F. Carlson

    1. Department of Mathematics, University of Georgia, Athens, USA

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Part of the book series: Lectures in Mathematics. ETH Zürich (LM)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xi
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  2. Augmentations, nilpotent ideals, and semisimplicity

    • Jon F. Carlson
    Pages 2-5

  3. Tensor products, Homs, and duality

    • Jon F. Carlson
    Pages 5-8

  4. Restriction and induction

    • Jon F. Carlson
    Pages 9-12

  5. Projective resolutions and cohomology

    • Jon F. Carlson
    Pages 12-17

  6. The stable category

    • Jon F. Carlson
    Pages 17-26

  7. Products in cohomology

    • Jon F. Carlson
    Pages 26-42

  8. Examples and diagrams

    • Jon F. Carlson
    Pages 42-52

  9. Relative projectivity

    • Jon F. Carlson
    Pages 53-58

  10. Relative projectivity and ideals in cohomology

    • Jon F. Carlson
    Pages 58-63

  11. Varieties and modules

    • Jon F. Carlson
    Pages 64-68

  12. Infinitely generated modules

    • Jon F. Carlson
    Pages 68-72

  13. Idempotent modules

    • Jon F. Carlson
    Pages 72-79

  14. Varieties and induced modules

    • Jon F. Carlson
    Pages 79-84

  15. Back Matter

    Pages 85-92
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Georgia, Athens, USA

    Jon F. Carlson

Bibliographic Information

  • Book Title: Modules and Group Algebras

  • Authors: Jon F. Carlson

  • Series Title: Lectures in Mathematics. ETH Zürich

  • DOI: https://doi.org/10.1007/978-3-0348-9189-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag, Basel, Switzerland 1996

  • Softcover ISBN: 978-3-7643-5389-6Published: 29 February 1996

  • eBook ISBN: 978-3-0348-9189-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 92

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Algebra

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