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1 results

Unistructurality of cluster algebras
Part of
- Arithmetic rings and other special rings
Peigen Cao, Fang Li
Journal:

Compositio Mathematica / Volume 156 / Issue 5 / May 2020

Published online by Cambridge University Press:

17 April 2020, pp. 946-958

Print publication:

May 2020
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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 ${\mathcal{A}}({\mathcal{S}})$.