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.

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 cha...

Table of Contents:

• 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.