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Green Functors and G-sets

  • Authors
  • Serge┬áBouc

Part of the Lecture Notes in Mathematics book series (LNM, volume 1671)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Serge Bouc
    Pages 1-3
  3. Serge Bouc
    Pages 5-39
  4. Serge Bouc
    Pages 41-60
  5. Serge Bouc
    Pages 123-152
  6. Serge Bouc
    Pages 153-165
  7. Serge Bouc
    Pages 167-182
  8. Serge Bouc
    Pages 183-222
  9. Serge Bouc
    Pages 223-274
  10. Serge Bouc
    Pages 275-304
  11. Serge Bouc
    Pages 305-336
  12. Back Matter
    Pages 337-342

About this book

Introduction

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.

Keywords

Algebra Equivalence Finite Group representation Representation theory categories category theory functors ring theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095821
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63550-5
  • Online ISBN 978-3-540-69596-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site