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Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Cambridge Studies in Advanced Mathematics)by D. Benson
Synopses & ReviewsPublisher Comments:The second of two volumes, Representation Theory and Cohomology, provides an introduction to the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras. The author emphasizes modular representations and the homological algebra associated with their categories. This volume concentrates on the cohomology of groups, always however, with representation in view. It begins with a background reference chapter, then proceeds to an overview of the algebraic topology and Ktheory associated with cohomology of groups, especially the work of Quillen. Later chapters look at algebraic and topological proofs of the finite generation of the cohomology ring of a finite group and an algebraic approach to the Steenrod operations in group cohomology. The book culminates with a chapter on the theory of varieties for modules.
Synopsis:This is the second of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras. Much of the material presented here has never appeared before in book form.
Synopsis:A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Synopsis:Now in paperback this is the first of two volumes that will provide an introdcution to modern developments in the representation theory of f inite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of representations of finite dimensional algebras; the author emphasises modular representations and the homological algebra associated with their categories.The heart of the book is a lengthy introduction to the represntation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail.
Synopsis:The heart of the book is a lengthy introduction to the representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail.
Synopsis:Author D. Benson concentrates on the cohomology of groups, always with representations in view. He also gives an overview of the algebraic topology and Ktheory associated with the cohomology of groups and discusses algebraic and topological proofs of the finite generation of the cohomology ring of a finite group. Students and researchers will appreciate this exposition on the essential results of modern representation theory.
Table of ContentsConventions and notations; Introduction; 1. Background material from algebraic topology; 2. Cohomology of groups; 3. Spectral sequences; 4. The Evens norm map and the Steenrod algebra; 5. Varieties for modules and multiple complexes; 6. Group actions and the Steinberg module; 7. Local coefficients on subgroup complexes; Bibliography; Index.
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