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Representations and Cohomology : Volume 2, Cohomology of Groups and Modules - No Information Available

Representations and Cohomology

Volume 2, Cohomology of Groups and Modules

By: No Information Available

Paperback | 17 August 1998

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This is the second of two volumes which will provide an introduction to modern developments in 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 emphasises modular representations and the homological algebra associated with their categories. This volume concentrates on the cohomology of groups, always with representations in view, however. It begins with a background reference chapter, then proceeds to an overview of the algebraic topology and K-theory 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 cumulates in a chapter dealing with the theory of varieties for modules. Much of the material presented here has never appeared before in book form. Consequently students and research workers studying group theory, and indeed algebra in general, will be grateful to Dr Benson for supplying an exposition of a good deal of the essential results of modern representation theory.
Industry Reviews
."..will certainly have a considerable influence on the further development of the subject." B. K^D"ulshammer, Zentralblatt f^D"ur Mathematik und ihre Grenzgebiete "It will surely give the research area of 'group cohomology' new impetus. It contains most of the results known about cohomology of groups, much of which had previously only been available in research papers." K.W. Roggenkamp, Mathematical Reviews "Benson's exposition is locally clear and engaging...his books are ideally suited for a graduate student or practicing group theorist who wants to reach the current research frontier rapidly. All in all, Benson has done an admirable job of drawing together the most important current ideas relating group representations to topology and group cohomology." J.E. Humphreys, Bulletin of the American Mathematical Society

You Can Find This Book In

Non-FictionMathematicsGroups & Group TheoryAlgebraTopologyAlgebraic TopologyNumber Theory

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Published: 20th May 1991

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