A conjecture on cluster automorphisms of cluster algebras

Peigen Cao; Fang Li; Siyang Liu; Jie Pan; Peigen Cao; Fang Li; Siyang Liu; Jie Pan

doi:10.3934/era.2019006

Electronic Research Archive

2019, Volume 27, 1-6. doi: 10.3934/era.2019006

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A conjecture on cluster automorphisms of cluster algebras

Department of Mathematics, Zhejiang University (Yuquan Campus), Hangzhou, Zhejiang, 310027, China

Received: 01 July 2019 Revised: 01 August 2019
Primary: 13F60

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.
- Cluster algebra,
- cluster automorphism
Citation: Peigen Cao, Fang Li, Siyang Liu, Jie Pan. A conjecture on cluster automorphisms of cluster algebras[J]. Electronic Research Archive, 2019, 27: 1-6. doi: 10.3934/era.2019006

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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.

References

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