On the local structure of Morita and Rickard equivalences between Brauer blocks
By: Lluís Puig
Series: Progress in mathematics -- v. 178; Progress in mathematics (Boston, Mass.) -- v. 178.
Publisher: Springer
Published: 1999
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 260
ISBN-13: 9783034886932; 9783034897327
Subjects: Finite groups; Representations of groups
Description: 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.
Notes: Originally published by Birkhäuser Verlag in 1999.

Softcover reprint of the hardcover 1st edition 1999.

Includes bibliographical references (p. [259]-260) and index.
Table of contents: title: Section 1. Introduction; title: section 2. General notation, terminology and quoted results; title: section 3. Noninjective induction of OG-interior algebras; title: section 4. Hecke OG-interior algebras and noninjective induction; title: section 5. On the local structure of Hecke OG-interior algebras; title: section 6. Morita stable equivalences between Brauer blocks; title: section 7. Basic Morita stable equivalences between Brauer blocks; title: section 8. The Morita stable equivalent class of a nilpotent block; title: section 9. The differential Z-grading O-algebra; title: section 10. DG-modules; title: section 11. D-algebras and DG-interior algebras; title: section 12. Induction of DG-interior algebras; title: section 13. Brauer sections in basic induced DG-interior algebras; title: section 14. Pointed groups on DG-interior algebras and Higman embeddings; title: section 15. Hecke DG-interior algebras and noninjective induction; title: section 16. On the local structure of Hecke DG-interior algebras; title: section 17. Brauer sections in basic Hecke DG-interior algebras; title: section 18. Rickard equivalences between Brauer blocks; title: section 19. Basic Rickard equivalences between Brauer blocks.