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Record Nr. |
UNISA996466864103316 |
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Autore |
König Steffen <1961-> |
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Titolo |
Derived equivalences for group rings / / Steffen König, Alexander Zimmermann with contributions by Bernhard Keller |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer, , [1998] |
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©1998 |
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ISBN |
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Edizione |
[1st ed. 1998.] |
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Descrizione fisica |
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1 online resource (X, 246 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1685 |
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Disciplina |
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Soggetti |
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Group rings |
Algebra, Homological |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages [233]-243) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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. |
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