Representations and Cohomology: Volume 2, Cohomology of Groups and Modules
Seiten
1998
Cambridge University Press (Verlag)
978-0-521-63652-0 (ISBN)
Cambridge University Press (Verlag)
978-0-521-63652-0 (ISBN)
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.
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.
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.
Conventions 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.
| Erscheint lt. Verlag | 18.6.1998 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 230 mm |
| Gewicht | 403 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-521-63652-3 / 0521636523 |
| ISBN-13 | 978-0-521-63652-0 / 9780521636520 |
| Zustand | Neuware |
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