Cluster automorphism groups and automorphism groups of exchange graphs

摘要

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