Auslander-Buchweitz approximations of equivariant modules

Author(s)

Bibliographic Information

Auslander-Buchweitz approximations of equivariant modules

Mitsuyasu Hashimoto

（London Mathematical Society lecture note series, 282）

Cambridge University Press, 2000

  • : pbk

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Note

Includes bibliographical references (p. [267]-276) and index

Description and Table of Contents

Description

This book, first published in 2000, focuses on homological aspects of equivariant modules. It presents a 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 co-algebras over an arbitrary base. It aims to overcome the difficulty of generalising known homological results in representation theory. This book will be of interest to researchers and graduate students in algebra, specialising in commutative ring theory and representation theory.

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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