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 $\mathcal A(S)$.

中文翻译：

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簇代数的单结构性

我们证明了任何偏对称簇代数都是单结构的，这是 Assem、Schiffler 和 Shramchenko 的猜想。作为推论，我们得到簇代数 $\mathcal A(\mathcal S)$ 的簇自同构只是环境场 $\mathcal F$ 的自同构，它限制为 $\mathcal A 的簇变量的置换(S)$。