Lectures on Block Theory

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Cambridge University Press, Apr 4, 1991 - Mathematics - 105 pages
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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.
 

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Contents

Foundations
1
Idempotents
5
Simple and Semisimple Algebras
12
Points and Maximal Ideals
18
Miscellaneous Results on Algebras
25
Modules
29
Groups Acting on Algebras
35
Pointed Groups
41
Group Algebras
63
Blocks of Group Algebras
68
Nilpotent Blocks
77
The Source Algebra of a Nilpotent Block
81
Puigs Theorem
91
Bibliography
94
Subject Index
97
List of Symbols
103

Sylow Theorems
46
Groups in Algebras
53

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Page 95 - On the structure of block ideals in group algebras of finite groups, Comm. Algebra 8 (1980), 1867-1872 18.
Page 95 - T. Okuyama and Y. Tsushima, Local properties of p-block algebras of finite groups, Osaka J. Math. 20 (1983), 33-41.
Page 94 - Group representation theory Part A," Marcel Dekker, New York 1971 11. L. DORNHOFF, "Group representation theory Part B," Marcel Dekker, New York 1972 12.
Page 94 - Methods of representation theory Vol. I," Wiley-Interscience, New York 1981 9. CW CURTIS and I. REINER, "Methods of representation theory Vol.
Page 94 - The Representation Theory of Finite Groups, North-Holland, Amsterdam, 1982. 13. W. Feit, M. Hall, and }. G. Thompson, "Finite groups in which the centrali2er of any non-identity element is nilpotent,
Page 95 - B. KULSHAMMER, Crossed products and blocks with normal defect groups, Comm. Algebra 13 (1985), 147-168.

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