Are cluster automorphism groups finitely generated?
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910266063585280 |
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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 |