Green Functors and G-sets

Serge Bouc (auth.)3540635505, 9783540635505

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.

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Table of contents :
Introduction….Pages 1-3
Mackey functors….Pages 5-39
Green functors….Pages 41-60
The category associated to a green functor….Pages 61-80
The algebra associated to a green functor….Pages 81-97
Morita equivalence and relative projectivity….Pages 99-121
Construction of green functors….Pages 123-152
A morita theory….Pages 153-165
Composition….Pages 167-182
Adjoint constructions….Pages 183-222
Adjunction and green functors….Pages 223-274
The simple modules….Pages 275-304
Centres….Pages 305-336