A note on cluster automorphism groups

Abstract

We conjecture a characterization of a cluster automorphism as an algebra homomorphism from the cluster algebra to itself that restricts to a bijection between two clusters. This formulation does not require that the map commutes with mutations as in the original definition of cluster automorphisms. We prove the conjecture in the case where at least one of the two clusters is bipartite.

This paper has been withdrawn by the authors, since there was a gap in the proof. The conjecture stated in the original version does not hold