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arXiv · 1609.02168

Strongness of companion bases for cluster-tilted algebras of finite type

Karin Baur·Alireza Nasr-Isfahani
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Abstract

For every cluster-tilted algebra of simply-laced Dynkin type we provide a companion basis which is strong, i.e. gives the set of dimension vectors of the finitely generated indecomposable modules for the cluster-tilted algebra. This shows in particular that every companion basis of a cluster-tilted algebra of simply-laced Dynkin type is strong. Thus we give a proof of Parsons's conjecture.

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BibTeXRIS

Karin Baur, Alireza Nasr-Isfahani. 2016-09-07. Strongness of companion bases for cluster-tilted algebras of finite type. https://doi.org/10.1090/proc/13977

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