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Full Description
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.
Contents
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.
