RUS  ENG
Full version
JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2020 Volume 16, 025, 22 pp. (Mi sigma1562)

This article is cited in 1 paper

Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

Tsukasa Ishibashi

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

Abstract: We give a method to compute presentations of saturated cluster modular groups. Using this, we obtain finite presentations of the saturated cluster modular groups of finite mutation type $X_6$ and $X_7$. We verify that the cluster modular groups of finite mutation type $\widetilde{E}_6$, $\widetilde{E}_7$, $\widetilde{E}_8$, $G_2^{(*,*)}$, $X_6$ and $X_7$ are virtually generated by cluster Dehn twists.

Keywords: cluster algebras, cluster modular groups, mapping class groups, quivers of finite mutation type.

MSC: 13F60, 05E15, 30F60

Received: January 1, 2020; in final form March 27, 2020; Published online April 7, 2020

Language: English

DOI: 10.3842/SIGMA.2020.025



Bibliographic databases:
ArXiv: 1711.07785


© Steklov Math. Inst. of RAS, 2025