Abstract
We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let Q be the Gabriel 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 Mut(Q) of Q such that \(Q^{\prime }\) admits a maximal green sequence. Furthermore, there is a quiver in Mut(Q) which does not admit a maximal green sequence if and only if \(\mathbb {X}\) is of wild type.
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We are very grateful to the anonymous referee for valuable comments.
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Presented by: Christof Geiss
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Partially supported by the National Natural Science Foundation of China (Grant No. 11971326, 12071315).
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Fu, C., Geng, S. On Maximal Green Sequence for Quivers Arising from Weighted Projective Lines. Algebr Represent Theor 26, 1713–1729 (2023). https://doi.org/10.1007/s10468-022-10152-3
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DOI: https://doi.org/10.1007/s10468-022-10152-3