Lecture Notes in Mathematics

By: serge Bouc

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Paperback | 10 October 1997

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352 Pages

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22.86 x 15.24 x 1.91

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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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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Algebra Calculus & Mathematical Analysis Functional Analysis & Transforms Mathematical Foundation Topology Algebraic Topology

Mackey functors	p. 5
Green functors	p. 41
The category associated to a Green functor	p. 61
The algebra associated to a Green functor	p. 81
Morita equivalence and relative projectivity	p. 99
Construction of Green functors	p. 123
A Morita theory	p. 153
Composition	p. 167
Adjoint constructions	p. 183
Adjunction and Green functors	p. 223
The simple modules	p. 275
Centres	p. 305
Bibliography	p. 337
Index	p. 339
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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