Derived Equivalences for Group Rings
Seiten
1998
|
1998
Springer Berlin (Verlag)
978-3-540-64311-1 (ISBN)
Springer Berlin (Verlag)
978-3-540-64311-1 (ISBN)
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.
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.
Erscheint lt. Verlag | 20.5.1998 |
---|---|
Reihe/Serie | Lecture Notes in Mathematics |
Co-Autor | B. Keller, M. Linckelmann, J. Rickard, R. Rouquier |
Zusatzinfo | X, 246 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 386 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
Schlagworte | Addition • character table • derived equivalences and derived categories • Equivalence • Finite • fundamental theorem • Grad • Group rings • Gruppe (Mathematik) • Proof • representations • Representation Theory • Theorem |
ISBN-10 | 3-540-64311-7 / 3540643117 |
ISBN-13 | 978-3-540-64311-1 / 9783540643111 |
Zustand | Neuware |
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