Abstract
We study the relation between the cluster automorphisms and the quasi-automorphisms of a cluster algebra A. We prove that under some mild condition, satisfied for example by every skew-symmetric cluster algebra, the quasi-automorphism group of A is isomorphic to a subgroup of the cluster automorphism group of Atriv, and the two groups are isomorphic if A has principal or universal coefficients; here Atriv is the cluster algebra with trivial coefficients obtained from A by setting all frozen variables equal to the integer 1.We also compute the quasi-automorphism group of all finite type and all skew-symmetric affine type cluster algebras, and show in which types it is isomorphic to the cluster automorphism group of Atriv.
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