Green Functors and G-sets

1997
ISBN: 978-3-540-63550-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1671, 342 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1090 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bouc, Serge

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.