A Course in Finite Group Representation Theory

This classroom-tested graduate text provides a thorough grounding in the representation theory of finite groups over fields and rings.

Peter Webb (Author)

9781107162396, Cambridge University Press

Hardback, published 19 August 2016

336 pages
23.5 x 15.8 x 2.3 cm, 0.62 kg

'The author aims to provide a comprehensive but fastpaced grounding in results which can be applied to areas as diverse as number theory, combinatorics, topology or commutative algebra … While the proofs are rigorous, the style is relatively informal and designed to showcase as many results as possible which are applicable beyond the realms of pure representation theory.' Stuart Martin, MathSciNet

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

1. Representations and Maschke's theorem
2. Algebras with semisimple modules
3. Characters
4. Construction of characters
5. Theorems of Mackey and Clifford
6. p-groups and the radical
7. Projective modules for algebras
8. Projective modules for group algebras
9. Splitting fields and the decomposition map
10. Brauer characters
11. Indecomposable modules
12. Blocks.

Subject Areas: Algebra [PBF]