# American Institute of Mathematical Sciences

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

## A conjecture on cluster automorphisms of cluster algebras

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

* Corresponding authors: Fang Li, Siyang Liu

Received  July 2019 Revised  August 2019 Published  August 2019

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.

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

show all references

##### References:
 [1] Hongyan Guo. Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra. Electronic Research Archive, , () : -. doi: 10.3934/era.2021008 [2] Nicola Pace, Angelo Sonnino. On the existence of PD-sets: Algorithms arising from automorphism groups of codes. Advances in Mathematics of Communications, 2021, 15 (2) : 267-277. doi: 10.3934/amc.2020065 [3] Qiang Fu, Xin Guo, Sun Young Jeon, Eric N. Reither, Emma Zang, Kenneth C. Land. The uses and abuses of an age-period-cohort method: On the linear algebra and statistical properties of intrinsic and related estimators. Mathematical Foundations of Computing, 2020  doi: 10.3934/mfc.2021001 [4] Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $\mathcal{W}(a, b, r)$. Electronic Research Archive, , () : -. doi: 10.3934/era.2020123

Impact Factor: 0.263