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arXiv · 1506.02029

Cluster automorphism groups and automorphism groups of exchange graphs

Wen Chang·Bin Zhu
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Abstract

For a coefficient free cluster algebra $\mathcal{A}$, we study the cluster automorphism group $Aut(\mathcal{A})$ and the automorphism group $Aut(E_{\mathcal{A}})$ of its exchange graph $E_{\mathcal{A}}$. We show that these two groups are isomorphic with each other, if $\mathcal{A}$ is of finite type excepting types of rank two and type $F_4$, or if $\mathcal{A}$ is of skew-symmetric finite mutation type.

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BibTeXRIS

Wen Chang, Bin Zhu. 2015-06-05. Cluster automorphism groups and automorphism groups of exchange graphs. https://doi.org/10.2140/pjm.2020.307.283

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