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This book presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of Delta-good approximations for quasi-hereditary algebras and reductive groups. The book provides a detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of coalgebras over an arbitrary base. It aims to overcome the difficulty of generalizing known homological results in representation theory.Read more
- A guide to equivariant modules
- Written by a leading researcher in the field
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"The reviewer enthusiastically recommends it for anyone, including beginners, who wants to see the Auslander-Buchweitz approximations in action." Mathematical Reviews
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- Date Published: November 2000
- format: Paperback
- isbn: 9780521796965
- length: 298 pages
- dimensions: 229 x 152 x 17 mm
- weight: 0.44kg
- availability: Available
Table of Contents
Conventions and terminology
Part I. Background Materials:
1. From homological algebra
2. From Commutative ring theory
3. Hopf algebras over an arbitrary base
4. From representation theory
5. Basics on equivariant modules
Part II. Equivariant Modules:
1. Homological aspects of (G, A)-modules
2. Matijevic-Roberts type theorem
Part III. Highest Weight Theory:
1. Highest weight theory over a field
2. Donkin systems
3. Ringel's theory over a field
4. Ringel's theory over a commutative ring
Part IV. Approximations of Equivariant Modules
1. Approximations of (G, A)-modules
2. An application to determinantal rings
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