The cluster-automorphism generation conjecture for noncommutative surface algebras

Let $\Sigma$ be a marked surface, let ${\mathcal A}_\Sigma$ be its noncommutative cluster algebra, and let $I_{p,1}(\Sigma)$ denote the set of the relevant once-punctured indices. In the notation of Remark, let the surface automorphisms be the automorphisms induced by surface symmetries, and let $\varphi_p$ be the additional automorphism associated with $p$. Cluster-automorphism generation conjecture. The group of cluster automorphisms of ${\mathcal A}_\Sigma$ is generated by the surface automorphisms and the elements $\varphi_p$ for $p\in I_{p,1}(\Sigma)$. The statement extends the known untagged result to the tagged/noncommutative setting described in the paper.