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Abstract
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For a coefficient-free cluster algebra
,
we study the cluster automorphism group
and the automorphism
group
of its
exchange graph
.
We show that these two groups are isomorphic with each other, if
is of finite type excepting types of rank 2 and type
, or
if
is
of skew-symmetric finite mutation type.
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Keywords
cluster algebra, cluster automorphism group, exchange graph
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Mathematical Subject Classification 2010
Primary: 13F60
Secondary: 05E40
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Milestones
Received: 20 June 2019
Revised: 27 January 2020
Accepted: 4 May 2020
Published: 4 September 2020
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