Unistructurality of cluster algebras of type (A)over-tilde

作者：Bazier Matte Veronique^*

来源：Journal of Algebra, 2016, 464: 297-315.

DOI：10.1016/j.jalgebra.2016.06.026

• Cluster algebras
• Unistructurality
• Triangulations
• Algebras arising from surfaces

It is conjectured by Assem, Schiflier and Shramchenko in [3] that every cluster algebra is unistructural, that is to say, that the set of cluster variables determines uniquely the cluster algebra structure. In other words, there exists a unique decomposition of the set of cluster variables into clusters. This conjecture has been proven to hold true for algebras of Dynkin type or rank 2, see [3]. The aim of this paper is to prove it for algebras of type (A) over tilde. We use triangulations of annuli and algebraic independence of clusters to prove unistructurality for algebras arising from annuli, which are of type (A) over tilde. We also prove the automorphism conjecture from [3] for algebras of type (A) over tilde as a direct consequence.

• 出版日期2016-10-15