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Paper   IPM / M / 15521
School of Mathematics
  Title:   Strongness of companion bases for cluster-tilted algebras of finite type
  Author(s):  Alireza Nasr-Isfahani (Joint with K. Baur)
  Status:   Published
  Journal: Proc. Amer. Math. Soc.
  Vol.:  146
  Year:  2018
  Pages:   2409-2416
  Supported by:  IPM
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 clustertilted algebra of simply-laced Dynkin type is strong. Thus we give a proof of Parsons’s conjecture.

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