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Unistructurality of cluster algebras

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arxiv 1809.05116 v2 pith:T3C3Y2PO submitted 2018-09-13 math.RT math.ACmath.RA

Peigen Cao , Fang Li This is my paper · ORCID
classification math.RTmath.ACmath.RA
keywords clustermathcalalgebraautomorphismalgebrasambientassemconjecture
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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 cluster variables of $\mathcal A(S)$.

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  1. A conjecture on cluster automorphisms of cluster algebras

    math.RT 2019-08 conditional novelty 7.0 of 10

    The paper proves that any Z-algebra homomorphism of a cluster algebra mapping one cluster to another is a cluster automorphism, confirming Chang-Schiffler's conjecture.

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