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

For a coefficient-free cluster algebra 𝒜, we study the cluster automorphism group Aut(𝒜) and the automorphism group Aut(E𝒜) of its exchange graph  E𝒜. We show that these two groups are isomorphic with each other, if 𝒜 is of finite type excepting types of rank 2 and type F4, or if 𝒜 is of skew-symmetric finite mutation type.

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cluster algebra, cluster automorphism group, exchange graph
Mathematical Subject Classification 2010
Primary: 13F60
Secondary: 05E40
Received: 20 June 2019
Revised: 27 January 2020
Accepted: 4 May 2020
Published: 4 September 2020
Wen Chang
School of Mathematics and Information Science
Shaanxi Normal University
Department of Mathematical Sciences
Tsinghua University
Beijing China
Bin Zhu
Department of Mathematical Sciences
Tsinghua University