Graded quotients of path algebras: A local theory
type: Item
instance of: scholarly article
title: Graded quotients of path algebras: A local theory
zbMATH Open document ID: 0811.16010
DOI: 10.1016/0022-4049(94)90112-0
published in: Journal of Pure and Applied Algebra
publication date: 1995-04-23T00:00:00Z
review text: The paper is a discussion of quotient algebras of path algebras of quivers on which groups act. By defining some subcategories of the categories of graded modules for a subset of the given group and the consideration of the relation between them, a local theory of graded modules is introduced. In this way, the authors show that if a graded ring is a quotient of a path algebra with a partial group action then one may retrieve the original algebra from knowledge of the local theory. Also, almost split sequences for indecomposable graded modules of finite length are shown to exist. Some results on the theory of group-graded path algebras and their quotients are used as a basis of their discussion. For this one may see the first author's paper [Trans. Am. Math. Soc. 279, 297-310 (1983; Zbl 0536.16001)].
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16W50
zbMATH DE Number: 579996
zbMATH Keywords: quotient algebras
zbMATH Keywords: path algebras
zbMATH Keywords: quivers
zbMATH Keywords: categories of graded modules
zbMATH Keywords: graded ring
zbMATH Keywords: partial group action
zbMATH Keywords: almost split sequences
zbMATH Keywords: group-graded path algebras
author: E. L. Green
author: Eduardo N. Marcos
reviewed by: Changchang Xi
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90112-0
OpenAlex ID: W2043878783
cites work: Modules with cores and amalgamations of indecomposable modules
cites work: A criterion for relative global dimension zero with applications to graded rings
cites work: Graphs with Relations, Coverings and Group-Graded Algebras
cites work: Q5508993
cites work: An introduction to homological algebra
description: scientific article; zbMATH DE number 579996