Presentations of Cluster Modular Groups and Generation by Cluster Dehn Twists

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 ${\tilde{E}}_6$, ${\tilde{E}}_7$, ${\tilde{E}}_8$, $G_2^{(\ast ,\ast )}$, $X_6$ and $X_7$ are virtually generated by cluster Dehn twists.

References in corpus (2)

• The quantum dilogarithm and representations quantum cluster varieties
• Comments on Exchange Graphs in Cluster Algebras

Cited by in corpus (1)

• Cluster Modular Groups of Affine and Doubly Extended Cluster Algebras