Green functors and G-sets / Serge Bouc.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1671.Publication details: Berlin ; New York : Springer, ©1997. Description: 1 online resource (342 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540695967; 3540695966Subject(s): Green functors | Group rings | Finite groups | Green, Foncteurs de | Anneaux de groupes | Groupes finis | Finite groups | Green functors | Group rings | Endliche Gruppe | Gruppenring | Green-Funktor | K-theorie | Algebra associativa | Teoria dos grupos | Anneaux de groupes | Groupes finisGenre/Form: Electronic books. Additional physical formats: Print version:: Green functors and G-sets.DDC classification: 510 s | 512/.55 LOC classification: QA3 | .L28 no. 1671Other classification: 31.21 | SI 850 | SK 230 | SK 260 | MAT 182f Online resources: Click here to access online
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Includes bibliographical references (pages 337-338) and index.
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 -- Bibliography -- Index.
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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