Cluster automorphism groups and automorphism groups of exchange graphs

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

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Keywords

cluster algebra, cluster automorphism group, exchange graph

Mathematical Subject Classification 2010

Primary: 13F60

Secondary: 05E40

Milestones

Received: 20 June 2019

Revised: 27 January 2020

Accepted: 4 May 2020

Published: 4 September 2020

Authors

Wen Chang
School of Mathematics and Information Science Shaanxi Normal University Xian China	Department of Mathematical Sciences Tsinghua University Beijing China

Bin Zhu
Department of Mathematical Sciences Tsinghua University Beijing China

Vol. 307, No. 2, 2020

Wen Chang and Bin Zhu

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors