Constructing tilted algebras from cluster-tilted algebras.
type: Item
instance of: scholarly article
title: Constructing tilted algebras from cluster-tilted algebras.
zbMATH Open document ID: 1242.16012
author: Marco Angel Bertani-Økland
author: Steffen Oppermann
author: Anette Wrålsen
published in: Journal of Algebra
publication date: 2010-06-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/0902.1667
review text: It was proven by \textit{I. Assem, T. Brüstle} and \textit{R. Schiffler} [Bull. Lond. Math. Soc. 40, No. 1, 151-162 (2008; Zbl 1182.16009)] that any cluster-tilted algebra can be obtained from a tilted algebra as a certain semi-direct product called the ``relation extension'' of the tilted algebra. There is not a one-to-one correspondence between tilted algebras and cluster-tilted algebras; several tilted algebras may have isomorphic relation extensions. The article under review provides an algorithm to determine all tilted algebras whose relation extension is a given cluster-tilted algebra of finite type. There are several well-presented examples to illustrate the algorithm and the theory necessary to carry it out.
reviewed by: Ryan Kinser
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 13F60
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16G70
zbMATH DE Number: 5716393
zbMATH Keywords: tilted algebras
zbMATH Keywords: cluster-tilted algebras
zbMATH Keywords: local slices
zbMATH Keywords: APR-tilting
zbMATH Keywords: finite-dimensional algebras
zbMATH Keywords: relation-extension algebras
zbMATH Keywords: trivial extensions
zbMATH Keywords: quivers
MaRDI profile type: Publication
OpenAlex ID: W2059688204
arXiv ID: 0902.1667
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DOI: 10.1016/J.JALGEBRA.2010.02.026
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description: scientific article