03007nam 22006615 450 991014629260332120250801064923.03-540-69596-610.1007/BFb0095821(CKB)1000000000437342(SSID)ssj0000323638(PQKBManifestationID)12091409(PQKBTitleCode)TC0000323638(PQKBWorkID)10300100(PQKB)11251669(DE-He213)978-3-540-69596-7(MiAaPQ)EBC5610930(Au-PeEL)EBL5610930(OCoLC)1078997172(MiAaPQ)EBC6842055(Au-PeEL)EBL6842055(OCoLC)1159612263(PPN)155184555(EXLCZ)99100000000043734220121227d1997 u| 0engurnn|008mamaatxtccrGreen Functors and G-sets /by serge Bouc1st ed. 1997.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1997.1 online resource (VII, 342 p.) Lecture Notes in Mathematics,1617-9692 ;1671Bibliographic Level Mode of Issuance: Monograph3-540-63550-5 Includes bibliographical references 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.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.Lecture Notes in Mathematics,1617-9692 ;1671K-theoryGroup theoryK-TheoryGroup Theory and GeneralizationsK-theory.Group theory.K-Theory.Group Theory and Generalizations.512.55Bouc Serge1955-61645MiAaPQMiAaPQMiAaPQBOOK9910146292603321Green functors and G-sets78122UNINA