Auslander-Buchweitz Approximations of Equivariant Modules
1st Edition
Published on 4. April 2011
978-0-511-89451-0 (ISBN)
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.
Reviews / Votes
'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.' EMSMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
30,31 MB
ISBN-13
978-0-511-89451-0 (9780511894510)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Mitsuyasu Hashimoto
Auslander-Buchweitz Approximations of Equivariant Modules
Book
11/2000
Cambridge University Press
€79.40
Shipment within 15-20 days
Person
Content
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.
