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© 1999

On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

Book
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Part of the Progress in Mathematics book series (PM, volume 178)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Lluís Puig Carreres
    Pages 1-7
  3. Lluís Puig Carreres
    Pages 9-21
  4. Lluís Puig Carreres
    Pages 23-35
  5. Lluís Puig Carreres
    Pages 47-59
  6. Lluís Puig Carreres
    Pages 61-72
  7. Lluís Puig Carreres
    Pages 93-101
  8. Lluís Puig Carreres
    Pages 103-111
  9. Lluís Puig Carreres
    Pages 113-122
  10. Lluís Puig Carreres
    Pages 123-131
  11. Lluís Puig Carreres
    Pages 133-149
  12. Lluís Puig Carreres
    Pages 175-180
  13. Lluís Puig Carreres
    Pages 181-197
  14. Lluís Puig Carreres
    Pages 199-213
  15. Lluís Puig Carreres
    Pages 215-228
  16. Lluís Puig Carreres
    Pages 229-242

About this book

Introduction

Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups.
In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence.
This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.

Keywords

Equivalence Finite Group theory Gruppentheorie Invariant algebra classification group set

Authors and affiliations

  1. 1.CNRS, Institut de Mathématiques de JussieuUniversité Denis Diderot (Paris VII)Paris Cedex 05France

Bibliographic information

  • Book Title On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks
  • Authors Lluis Puig
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-8693-2
  • Copyright Information Birkhäuser Verlag 1999
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6156-3
  • Softcover ISBN 978-3-0348-9732-7
  • eBook ISBN 978-3-0348-8693-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages VII, 261
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site

Reviews

"The author investigates the behavior of the local structure of a block under Morita equivalences, stable equivalences of Morita type (called Morita stable equivalences here) and Rickard equivalences. The local structure of a block is expressed mainly in terms of its local category (consisting of local pointed groups and their exomorphisms), its Brauer category (consisting of Brauer pairs and their exomorphisms) and its source algebra."

–Zentralblatt Math