Derived Equivalences for Group Rings

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Alexander Zimmermann works on equivalences between derived module categories, stable module categories, Hochschild cohomology and integral and modular representations of groups.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	1998
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	Einband - flex.(Paperback)
ISBN-13:	9783540643111
ISBN-10:	3540643117
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	König, Steffen Zimmermann, Alexander
Hersteller:	Springer Springer Vieweg Springer-Verlag GmbH Lecture Notes in Mathematics
Verantwortliche Person für die EU:	Springer Nature Customer Service Center GmbH, Europaplatz 3, D-69115 Heidelberg, productsafety@springernature.com
Maße:	235 x 155 x 15 mm
Von/Mit:	Steffen König (u. a.)
Erscheinungsdatum:	20.05.1998
Gewicht:	0,4 kg