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

Baur, Karin; Nasr-Isfahani, Alireza

doi:10.1090/proc/13977

Strongness of companion bases for cluster-tilted algebras of finite type
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by Karin Baur and Alireza Nasr-Isfahani PDF

Proc. Amer. Math. Soc. 146 (2018), 2409-2416 Request permission

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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