#### Vol. 307, No. 2, 2020

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Cluster automorphism groups and automorphism groups of exchange graphs

### Wen Chang and Bin Zhu

Vol. 307 (2020), No. 2, 283–302
##### Abstract

For a coefficient-free cluster algebra $\mathsc{𝒜}$, we study the cluster automorphism group $Aut\left(\mathsc{𝒜}\right)$ and the automorphism group $Aut\left({E}_{\mathsc{𝒜}}\right)$ of its exchange graph  ${E}_{\mathsc{𝒜}}$. We show that these two groups are isomorphic with each other, if $\mathsc{𝒜}$ is of finite type excepting types of rank 2 and type ${F}_{4}$, or if $\mathsc{𝒜}$ is of skew-symmetric finite mutation type.

##### Keywords
cluster algebra, cluster automorphism group, exchange graph
Primary: 13F60
Secondary: 05E40