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Derived Equivalences for Group Rings

  • Book
  • © 1998

Overview

Authors:
  1. Steffen König
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  2. Alexander Zimmermann
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1685)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Alexander Zimmermann
    Pages 1-4

  3. Basic definitions and some examples

    • Steffen König
    Pages 5-32

  4. Rickard's fundamental theorem

    • Steffen König
    Pages 33-50

  5. Some modular and local representation theory

    • Alexander Zimmermann
    Pages 51-80

  6. Onesided tilting complexes for group rings

    • Alexander Zimmermann
    Pages 81-104

  7. Tilting with additional structure: twosided tilting complexes

    • Alexander Zimmermann
    Pages 105-149

  8. Historical remarks

    • Alexander zimmermann
    Pages 151-154

  9. On the construction of triangle equivalences

    • Bernhard Keller
    Pages 155-176

  10. Triangulated categories in the modular representation theory of finite groups

    • Jeremy Rickard
    Pages 177-198

  11. The derived category of blocks with cyclic defect groups

    • Raphaël Rouquier
    Pages 199-220

  12. On stable equivalences of Morita type

    • Markus Linckelmann
    Pages 221-232

  13. Back Matter

    Pages 233-246
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Derived Equivalences for Group Rings

  • Authors: Steffen König, Alexander Zimmermann

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096366

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-64311-1Published: 20 May 1998

  • eBook ISBN: 978-3-540-69748-0Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 246

  • Topics: Group Theory and Generalizations, K-Theory

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