English

Cluster Automorphisms

Representation Theory 2014-02-26 v2 Rings and Algebras

Abstract

In this article, we introduce the notion of cluster automorphism of a given cluster algebra as a \ZZ\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.

Keywords

Cite

@article{arxiv.1009.0742,
  title  = {Cluster Automorphisms},
  author = {Ibrahim Assem and Ralf Schiffler and Vasilisa Shramchenko},
  journal= {arXiv preprint arXiv:1009.0742},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T16:09:17.537Z