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Unistructurality of cluster algebras

Published online by Cambridge University Press:  17 April 2020

Peigen Cao
Affiliation:
Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou,Zhejiang310027, PR China Université de Paris, UFR de Mathématiques, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, Batiment Sophie Germain, 75205 Paris Cedex 13, France email [email protected]
Fang Li
Affiliation:
Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou, Zhejiang310027, PR China email [email protected]

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 ${\mathcal{A}}({\mathcal{S}})$.

MSC classification

Type
Research Article
Copyright
© The Authors 2020

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