Constructing tilted algebras from cluster-tilted algebras
Representation Theory
2010-05-04 v2 Rings and 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.
Cite
@article{arxiv.0902.1667,
title = {Constructing tilted algebras from cluster-tilted algebras},
author = {Marco Angel Bertani-Økland and Steffen Oppermann and Anette Wrålsen},
journal= {arXiv preprint arXiv:0902.1667},
year = {2010}
}
Comments
Section 3 has been removed and now is an independent article (arXiv:0912.2911v1). Section 1 and 2.2 have been modified to cope with the removal of section 3. Proof of theorem 3.5 (previously 4.5) has been improved. More details have been added to section 6 (previously 7) to clarify how section 3 (previously 4) generalizes to the infinite case