On maximal green sequence for quivers arising from weighted projective lines

Abstract

We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver of the endomorphism algebra of a basic cluster-tilting object in the cluster category ${\mathcal{C}}_{\mathbb{X}}$ of a weighted projective line $\mathbb{X}$. It is proved that there exists a quiver $Q^{\prime }$ in the mutation equivalence class $\mathrm{Mut}(Q)$ such that $Q^{\prime }$ admits a maximal green sequence. On the other hand, there is a quiver in $\mathrm{Mut}(Q)$ which does not admit a maximal green sequence if and only if $\mathbb{X}$ is of wild type.

Minor changes

References in corpus (6)

• On triangulated orbit categories
• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Periodicities in cluster algebras and dilogarithm identities
• A survey on maximal green sequences
• On cluster-tilting graphs for hereditary categories
• Uniformly column sign-coherence and the existence of maximal green sequences