Derived Equivalences for Group Rings [electronic resource] / by Steffen König, Alexander Zimmermann.
Material type: TextSeries: Lecture Notes in Mathematics ; 1685Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998Description: X, 246 p. online resourceContent type:- text
- computer
- online resource
- 9783540697480
- 512.2 23
- QA174-183
Basic definitions and some examples -- Rickard's fundamental theorem -- Some modular and local representation theory -- Onesided tilting complexes for group rings -- Tilting with additional structure: twosided tilting complexes -- Historical remarks -- On the construction of triangle equivalences -- Triangulated categories in the modular representation theory of finite groups -- The derived category of blocks with cyclic defect groups -- On stable equivalences of Morita type.
A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
There are no comments on this title.