A conjecture on cluster automorphisms of cluster algebras
arXiv:1908.02907
summary
The authors prove the Chang–Schiffler conjecture that every cluster automorphism of a cluster algebra is precisely a ℤ‑algebra homomorphism that maps one cluster to another and commutes with mutations.
Abstract
A cluster automorphism is a $\mathbb{Z}$-algebra automorphism of a cluster algebra $\mathcal A$ satisfying that it sends a cluster to another and commutes with mutations. Chang and Schiffler conjectured that a cluster automorphism of $\mathcal A$ is just a $\mathbb{Z}$-algebra homomorphism of a cluster algebra sending a cluster to another. The aim of this article is to prove this conjecture.
6 pages
Topics & keywords
#cluster algebras#automorphisms#mutations#conjecture proof#ℤ‑algebra homomorphismscluster automorphismcluster algebraℤ‑algebramutationChang–Schiffler conjecture