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CLUSTER AUTOMORPHISMS AND COMPATIBILITY OF CLUSTER VARIABLES
Glasgow Mathematical Journal
In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if A is unistructural or of Euclidean type, then f : A → A is a cluster automorphism if and only if f is an automorphism of the ambient field which restricts to a permutation of the cluster variables. In order to prove this result, we alsodoi:10.1017/s0017089514000214 fatcat:akzl3vzjpzbvvmsi6nmgwnbb5q