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This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.Read more
- Provides a detailed treatment of cornerstones in the subject that have not appeared in any book before
- Difficult foundational material is made accessible using new proofs
- Gives a comprehensive overview of the subject, useful for both students and researchers
Reviews & endorsements
'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the ﬁrst time. It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental open problems. It is well written and will certainly become a standard reference.' Burkhard Kűlshammer, MathSciNet
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- Date Published: May 2018
- format: Paperback
- isbn: 9781108441834
- length: 524 pages
- dimensions: 228 x 152 x 28 mm
- weight: 0.74kg
- contains: 75 exercises
- availability: Available
Table of Contents
1. Algebras and modules
2. Functors between module categories
3. Character theory
4. Algebras over p-local rings
5. Group algebras and modules over p-local rings
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