1.

Record Nr.

UNISA996466864103316

Autore

König Steffen <1961->

Titolo

Derived equivalences for group rings / / Steffen König, Alexander Zimmermann with contributions by Bernhard Keller

Pubbl/distr/stampa

Berlin, Germany ; ; New York, New York : , : Springer, , [1998]

©1998

ISBN

3-540-69748-9

Edizione

[1st ed. 1998.]

Descrizione fisica

1 online resource (X, 246 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1685

Disciplina

512.2

Soggetti

Group rings

Algebra, Homological

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (pages [233]-243) and index.

Nota di contenuto

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.

Sommario/riassunto

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.