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Green Functors and G-sets

  • Book
  • © 1997

Overview

Authors:
  1. Serge Bouc
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1671)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • Serge Bouc
    Pages 1-3
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  3. Mackey functors

    • Serge Bouc
    Pages 5-39
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  4. Green functors

    • Serge Bouc
    Pages 41-60
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  5. The category associated to a green functor

    • Serge Bouc
    Pages 61-80
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  6. The algebra associated to a green functor

    • Serge Bouc
    Pages 81-97
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  7. Morita equivalence and relative projectivity

    • Serge Bouc
    Pages 99-121
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  8. Construction of green functors

    • Serge Bouc
    Pages 123-152
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  9. A morita theory

    • Serge Bouc
    Pages 153-165
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  10. Composition

    • Serge Bouc
    Pages 167-182
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  11. Adjoint constructions

    • Serge Bouc
    Pages 183-222
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  12. Adjunction and green functors

    • Serge Bouc
    Pages 223-274
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  13. The simple modules

    • Serge Bouc
    Pages 275-304
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  14. Centres

    • Serge Bouc
    Pages 305-336
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  15. Back Matter

    Pages 337-342
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Keywords

About this book

This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets. Some classical constructions, such as the associated categroy or algebra, have a natural interpretation in that framework. Many notions of ring theory can be extended to Green functors (opposite Green functor, bimodules, Morita theory, simple modules, centres,...). There are moreover connections between Green functors for different groups, given by functors associated to bisets. Intended for researchers and students in representation theory of finite groups it requires only basic algebra and category theory, though knowledge of the classical examples of Mackey functors is probably preferable.

Bibliographic Information

  • Book Title: Green Functors and G-sets

  • Authors: Serge Bouc

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095821

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63550-5Published: 10 October 1997

  • eBook ISBN: 978-3-540-69596-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VII, 342

  • Topics: K-Theory, Group Theory and Generalizations

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