Periodicities in Cluster Algebras and Cluster Automorphism Groups

• 作者: Siyang Liu Fang Li
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 601-624
• 页数: 24页
• 语种: 英文
• DOI: 10.1142/S100538672100047X

摘要

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A) for a cluster algebra A and the group AutMn(S) for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.