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  3. Representations and Cohomology
  • Cited by 22
  • Volume 2: Cohomology of Groups and Modules
  • D. J. Benson, University of Georgia
Publisher:
Cambridge University Press
Online publication date:
February 2010
Print publication year:
1991
Online ISBN:
9780511623622
DOI:
https://doi.org/10.1017/CBO9780511623622
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
Cambridge Studies in Advanced Mathematics (31)
Information

Book description

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.

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