Cluster Automorphisms

Details Cluster Automorphisms Cluster Automorphisms

2010-09-03

arxiv.org/abs/1009.0742v2

Mathematics

Representation Theory

35 pages, v2 final version, to appear in Proc. London Math. Soc

Scientific paper

In this article, we introduce the notion of cluster automorphism of a given cluster algebra as a $\ZZ$-automorphism of the cluster algebra that sends a cluster to another and commutes with mutations. We study the group of cluster automorphisms in detail for acyclic cluster algebras and cluster algebras from surfaces, and we compute this group explicitly for the Dynkin types and the Euclidean types.

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