Are cluster automorphism groups finitely generated?

Fuente: arXiv
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Autori principali: Fu, Changjian, Liang, Zhanhong, Wang, Yinzhi
Natura: Preprint
Pubblicazione: 2026
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author Fu, Changjian
Liang, Zhanhong
Wang, Yinzhi
author_facet Fu, Changjian
Liang, Zhanhong
Wang, Yinzhi
contents This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely generated. As applications, we re-establish the finite generation of the automorphism groups for all finite mutation type cluster algebras, and verify the acyclic cases. Furthermore, we illustrate through examples that our approach significantly simplifies the computation of presentations for these groups in certain cases.
format Preprint
id arxiv_https___arxiv_org_abs_2605_16854
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Are cluster automorphism groups finitely generated?
Fu, Changjian
Liang, Zhanhong
Wang, Yinzhi
Rings and Algebras
Group Theory
13F60
This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely generated. As applications, we re-establish the finite generation of the automorphism groups for all finite mutation type cluster algebras, and verify the acyclic cases. Furthermore, we illustrate through examples that our approach significantly simplifies the computation of presentations for these groups in certain cases.
title Are cluster automorphism groups finitely generated?
topic Rings and Algebras
Group Theory
13F60
url https://arxiv.org/abs/2605.16854