Auslander-Buchweitz approximations of equivariant modules /
Mitsuyasu Hashimoto.
- Cambridge : Cambridge University Press, 2000.
- 1 online resource (xvi, 281 pages) : digital, PDF file(s).
- London Mathematical Society lecture note series ; 282 .
- London Mathematical Society lecture note series ; 282. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
From homological algebra -- From commutative ring theory -- Hopf algebras over an arbitrary base -- From representation theory -- Equivariant modules -- Homological aspects of (G, A)-modules -- Matijevic-roberts type theorem -- Highest weight theory -- Highest weight theory over a field -- Donkin systems -- Ringel's theory over field -- Ringel's theory over a commutative ring -- Approximations of equivariant modules -- Approximations of (G, A)-modules -- Application to determinantal rings.
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.