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Unistructurality of cluster algebras

  • Peigen Cao (a1) (a2) and Fang Li (a3)

Abstract

We prove that any skew-symmetrizable cluster algebra is unistructural, which is a conjecture by Assem, Schiffler and Shramchenko. As a corollary, we obtain that a cluster automorphism of a cluster algebra ${\mathcal{A}}({\mathcal{S}})$ is just an automorphism of the ambient field ${\mathcal{F}}$ which restricts to a permutation of the cluster variables of ${\mathcal{A}}({\mathcal{S}})$ .

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Unistructurality of cluster algebras

  • Peigen Cao (a1) (a2) and Fang Li (a3)

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