Auslander-Buchweitz Approximations of Equivariant Modules (London Mathematical Society Lecture Note Series, Series Number 282)

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 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 coalgebras over an arbitrary base. It aims to overcome the difficulty of generalizing known homological results in representation theory.

This book focuses on homological aspects of equivariant modules. It 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 delta-good approximations for quasi-hereditary algebras and reductive groups. It also provides detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of co-algebras over an arbitrary base. The book is primarily aimed at researchers but will also be suitable for graduate students.