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AuthorBouc, Serge. author
TitleGreen Functors and G-sets [electronic resource] / by Serge Bouc
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1997
Connect tohttp://dx.doi.org/10.1007/BFb0095821
Descript VII, 342 p. online resource

SUMMARY

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


CONTENT

Mackey functors -- Green functors -- The category associated to a green functor -- The algebra associated to a green functor -- Morita equivalence and relative projectivity -- Construction of green functors -- A morita theory -- Composition -- Adjoint constructions -- Adjunction and green functors -- The simple modules -- Centres


Mathematics Group theory K-theory Mathematics K-Theory Group Theory and Generalizations



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