E-Book, Englisch, Band 1685, 246 Seiten, eBook
Reihe: Lecture Notes in Mathematics
König / Zimmermann Derived Equivalences for Group Rings
Erscheinungsjahr 2006
ISBN: 978-3-540-69748-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 1685, 246 Seiten, eBook
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-69748-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Weitere Infos & Material
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.
