Lectures on Block Theory

Burkhard Külshammer

doi:10.1017/CBO9780511565786

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This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Ellers, Harald 1994. Cliques of irreducible representations ofp-solvable groups and a theorem analogous to Alperin’s conjecture. Mathematische Zeitschrift, Vol. 217, Issue. 1, p. 607.

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Külshammer, Burkhard 1994. Central idempotents in p-adic group rings. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 56, Issue. 2, p. 278.

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Hazewinkel, M. 1997. Encyclopaedia of Mathematics. p. 71.

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Kadison, Lars and Külshammer, Burkhard 2006. Depth Two, Normality, and a Trace Ideal Condition for Frobenius Extensions. Communications in Algebra, Vol. 34, Issue. 9, p. 3103.

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Boltje, Robert and Külshammer, Burkhard 2011. Group algebra extensions of depth one. Algebra & Number Theory, Vol. 5, Issue. 1, p. 63.

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黄, 文林 2013. On the Generalized Inflated G-Algebras. Pure Mathematics, Vol. 03, Issue. 01, p. 101.

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ERDMANN, KARIN and SKOWROŃSKI, ANDRZEJ 2020. ALGEBRAS OF GENERALIZED DIHEDRAL TYPE. Nagoya Mathematical Journal, Vol. 240, Issue. , p. 181.

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Margolis, Leo 2022. The Modular Isomorphism Problem: A Survey. Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 124, Issue. 3, p. 157.

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Burkhard Külshammer, Universität Augsburg

Publisher:: Cambridge University Press
Online publication date:: June 2011
Print publication year:: 1991
Online ISBN:: 9780511565786
DOI:: https://doi.org/10.1017/CBO9780511565786

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: London Mathematical Society Lecture Note Series (161)

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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.

"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

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Lectures on Block Theory

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Foundations
pp 1-4

2 - Idempotents
pp 5-11

3 - Simple and Semisimple Algebras
pp 12-17

4 - Points and Maximal Ideals
pp 18-24

5 - Miscellaneous Results on Algebras
pp 25-28

6 - Modules
pp 29-34

7 - Groups Acting on Algebras
pp 35-40

8 - Pointed Groups
pp 41-45

9 - Sylow Theorems
pp 46-52

10 - Groups in Algebras
pp 53-62

11 - Group Algebras
pp 63-67

12 - Blocks of Group Algebras
pp 68-76

13 - Nilpotent Blocks
pp 77-80

14 - The Source Algebra of a Nilpotent Block
pp 81-90

15 - Puig's Theorem
pp 91-93

Bibliography
pp 94-96

Subject Index
pp 97-102

List of Symbols
pp 103-105

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