Auslander-Buchweitz Approximations of Equivariant Modules

This book, first piblished in 2000, contains research on commutative ring theory and representation theory.

Mitsuyasu Hashimoto (Author)

9780521796965, Cambridge University Press

Paperback, published 2 November 2000

298 pages
22.9 x 15.2 x 1.7 cm, 0.44 kg

'This monograph brings the reader to the bounds of knowledge in the subject. It will be of interest of researchers and graduate students, both in commutative ring theory and representation theory.' EMS

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.

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.

Subject Areas: Algebra [PBF], Mathematics [PB]