On the quiver with relations of a repetitive algebra
type: Item
instance of: scholarly article
title: On the quiver with relations of a repetitive algebra
zbMATH Open document ID: 0937.16018
author: Jan Schröer
published in: Archiv der Mathematik
publication date: 2000-06-04T00:00:00Z
review text: Let \(A=kQ/(\rho)\) be a finite-dimensional \(k\)-algebra for the quiver \(Q\) with the set of relations \(\rho\) consisting only of zero- or commutativity-relations. The author describes explicitly the quiver of the repetitive algebra [\textit{D. Hughes, J. Waschbüsch}, Proc. Lond. Math. Soc., III. Ser. 46, 347-364 (1983; Zbl 0488.16021)] \(\widehat A\) of \(A\). It is also proved that \(A\) is gentle if and only if \(\widehat A\) is special biserial [\textit{C. M. Ringel}, Bol. Soc. Mat. Mex., III. Ser. 3, No.~2, 235-253 (1997; Zbl 0906.16005)].
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 1333330
zbMATH Keywords: gentle algebras
zbMATH Keywords: special biserial algebras
zbMATH Keywords: quivers
zbMATH Keywords: repetitive algebras
reviewed by: Feliks R. Bobovich
MaRDI profile type: Publication
full work available at URL: s000130050351
OpenAlex ID: W196786062
DOI: 10.1007/S000130050351
description: scientific article; zbMATH DE number 1333330