The Block Theory of Finite Group Algebras 2 Paperback Book Set (London Mathematical Society Student Texts)
Cambridge University Press, 5/24/2018
EAN 9781108441902, ISBN10: 1108441904
Paperback, 1114 pages, 22.6 x 15.2 x 5.6 cm
Language: English
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.
Volume 1
Introduction
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
References
Index. Volume 2
Introduction
6. Blocks and source algebras
7. Modules over finite p-groups
8. Local structure
9. Isometries and bimodules
10. Structural results in block theory
11. Blocks with cyclic defect groups
12. Blocks with Klein four defect groups
Appendix
References
Index.