Constructing tilted algebras from cluster-tilted algebras
Marco Angel Bertani-{\O}kland, Steffen Oppermann, Anette, Wr{\aa}lsen
TL;DR
This paper introduces a method to construct all tilted algebras from a given cluster-tilted algebra by analyzing the distribution of cluster-tilting objects in the Auslander-Reiten quiver.
Contribution
It provides a systematic way to derive tilted algebras from cluster-tilted algebras based on the cluster-tilting object distribution.
Findings
Method to construct tilted algebras from cluster-tilted algebras
Applicable to any cluster-tilted algebra with known cluster-tilting object distribution
Enhances understanding of the relationship between tilted and cluster-tilted algebras
Abstract
Any cluster-tilted algebra is the relation extension of a tilted algebra. We present a method to, given the distribution of a cluster-tilting object in the Auslander-Reiten quiver of the cluster category, construct all tilted algebras whose relation extension is the endomorphism ring of this cluster-tilting object.
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