Lectures on Block Theory

This textbook is intended as a self contained introduction into that part of algebra known as representation of finite groups.

Burkhard Külshammer (Author)

9780521405652, Cambridge University Press

Paperback, published 4 April 1991

116 pages
22.8 x 15.2 x 0.7 cm, 0.178 kg

"The clearly-written and well-presented text can be used for a one-semester course or a seminar on the subject. I should like to recommend this book to anyone who wishes to learn more about these fascinating new ideas and developments in the representation theory of finite groups." M. Geck, LMS

Block theory is a part of the theory of modular representation of finite groups and deals with the algebraic structure of blocks. In this volume Burkhard Külshammer starts with the classical structure theory of finite dimensional algebras, and leads up to Puigs main result on the structure of the so called nilpotent blocks, which he discusses in the final chapter. All the proofs in the text are given clearly and in full detail, and suggestions for further reading are also included. For researchers and graduate students interested in group theory or representation theory, this book will form an excellent self contained introduction to the theory of blocks.

1. Foundations
2. Idempotents
3. Simple and semi-simple algebras
4. Points and maximal ideals
5. Miscellaneous results on algebras
6. Modules
7. Groups acting on algebras
8. Pointed groups
9. Sylow theorems
10. Groups in algebras
11. Group algebras
12. Blocks of group algebras
13. Nilpotent blocks
14. The source algebra of a nilpotent block
15. Puigs theorem
Bibliography
Subject index
List of symbols.

Subject Areas: Algebra [PBF]