Derived Equivalences for Group Rings

• Main Authors: König, Steffen (Author, http://id.loc.gov/vocabulary/relators/aut), Zimmermann, Alexander (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Edition: 1st ed. 1998.
• Series: Lecture Notes in Mathematics, 1685
• Subjects: Group theory.; K-theory.; Group Theory and Generalizations.; K-Theory.
• Physical Description: X, 246 p. online resource.
• ISBN: 9783540697480
• ISSN: 0075-8434 ;
• DOI: 10.1007/BFb0096366

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.