Unfoldings and APR-tilts
type: Item
instance of: scholarly article
title: Unfoldings and APR-tilts
zbMATH Open document ID: 0804.16014
author: S. Brenner
author: Ibrahim Assem
published in: Journal of Algebra
publication date: 1995-01-12T00:00:00Z
review text: Let \(A\) be a finite dimensional, basic, connected, associative algebra with an identity over an algebraically closed field, and whose ordinary quiver has no oriented cycles. The authors give an effective criterion for determining whether or not \(A\) is iterated tilted of euclidean type or tilting-cotilting equivalent to a tubular canonical algebra. If \(A\) is representation-infinite, this problem is solved by \textit{I. Assem} and \textit{A. Skowroński} [in Math. Ann. 280, 441-463 (1988; Zbl 0617.16017)]. The presented algorithm is equivalent to that introduced by \textit{S. Brenner} [Proc. Lond. Math. Soc., III. Ser. 62, 242-274 (1991; Zbl 0679.16015)] and uses an unfolding tower of full additive subcategories of the homotopy category \(K^ b({\mathcal P}_ A)\) of bounded complexes of projective \(A\)-modules.
reviewed by: Andrzej Skowroński
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 16Z05
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 579542
zbMATH Keywords: finite dimensional, basic, connected, associative algebra
zbMATH Keywords: ordinary quiver
zbMATH Keywords: iterated tilted of euclidean type
zbMATH Keywords: tilting-cotilting equivalent to a tubular canonical algebra
zbMATH Keywords: representation-infinite
zbMATH Keywords: algorithm
zbMATH Keywords: unfolding tower
zbMATH Keywords: full additive subcategories
zbMATH Keywords: homotopy category
zbMATH Keywords: bounded complexes
MaRDI profile type: Publication
full work available at URL: jabr.1994.1082
OpenAlex ID: W1977463175
DOI: 10.1006/JABR.1994.1082
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description: scientific article; zbMATH DE number 579542