Auslander-Buchweitz Approximations of Equivariant Modules

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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 Δ-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.

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Editorial Reviews

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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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Product Details

Table of Contents

Introduction; 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; Bibliography; Index; Glossary.

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