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Finite Group Algebras and their Modules : London Mathematical Society Lecture Notes - P. Landrock

Finite Group Algebras and their Modules

London Mathematical Society Lecture Notes

Paperback

Published: 27th February 1984
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Originally published in 1983, the principal object of this book is to discuss in detail the structure of finite group rings over fields of characteristic, p, P-adic rings and, in some cases, just principal ideal domains, as well as modules of such group rings. The approach does not emphasize any particular point of view, but aims to present a smooth proof in each case to provide the reader with maximum insight. However, the trace map and all its properties have been used extensively. This generalizes a number of classical results at no extra cost and also has the advantage that no assumption on the field is required. Finally, it should be mentioned that much attention is paid to the methods of homological algebra and cohomology of groups as well as connections between characteristic 0 and characteristic p.

Preface
The Structure of Group Algebras
Idempotents in rings. Liftings
Projective and injective modules
The radical and artinian rings
Cartan invariants and blocks
Finite dimensional algebras
Duality
Symmetry
Loewy series and socle series
The p. i. m.'s
Ext
Orders
Modular systems and blocks
Centers
R-forms and liftable modules
Decomposition numbers and Brauer characters
Basic algebras and small blocks
Pure submodules
Examples
Indecomposable Modules and Relative Projectivity
The trace map and the Nakayama relations
Relative projectivity
Vertices and sources
Green Correspondence
Relative projective homomorphisms
Tensor products
The Green ring
Endomorphism rings
Almost split sequences
Inner products on the Green ring
Induction from normal subgroups
Permutation models
Examples
Block Theory
Blocks, defect groups and the Brauer map
Brauer's First Main Theorem
Blocks of groups with a normal subgroup
The Extended First main Theorem
Defect groups and vertices
Generalized decomposition numbers
Subpairs
Characters in blocks
Vertices of simple modules
Defect groups
Appendices
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521274876
ISBN-10: 0521274877
Series: London Mathematical Society Lecture Notes
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 286
Published: 27th February 1984
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.63
Weight (kg): 0.42