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AuthorKรถnig, Steffen. author
TitleDerived Equivalences for Group Rings [electronic resource] / by Steffen Kรถnig, Alexander Zimmermann
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1998
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Descript X, 246 p. online resource


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, Brouรฉ'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

Mathematics Group theory K-theory Mathematics Group Theory and Generalizations K-Theory


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