Mutation classes of certain quivers with potentials as derived equivalence classes

Abstract

We characterize the marked bordered unpunctured oriented surfaces with the property that all the Jacobian algebras of the quivers with potentials arising from their triangulations are derived equivalent. These are either surfaces of genus g with b boundary components and one marked point on each component, or the disc with 4 or 5 points on its boundary. We show that for each such marked surface, all the quivers in the mutation class have the same number of arrows, and the corresponding Jacobian algebras constitute a complete derived equivalence class of finite-dimensional algebras whose members are connected by sequences of Brenner-Butler tilts. In addition, we provide explicit quivers for each of these classes. We consider also 10 of the 11 exceptional finite mutation classes of quivers not arising from triangulations of marked surfaces excluding the one of the quiver X_7, and show that all the finite-dimensional Jacobian algebras in such class (for suitable choice of potentials) are derived equivalent only for the classes of the quivers E_6^(1,1) and X_6.

16 pages

References in corpus (6)

• Skew-symmetric cluster algebras of finite mutation type
• Combinatorial derived invariants for gentle algebras
• Mutation classes of \tilde{A}_n-quivers and derived equivalence classification of cluster tilted algebras of type \tilde{A}_n
• Perverse equivalences, BB-tilting, mutations and applications
• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
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Cited by in corpus (13)

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• The representation type of Jacobian algebras
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• On cluster algebras from once punctured closed surfaces
• Which mutation classes of quivers have constant number of arrows?
• Algebras of partial triangulations
• Analyticity and resurgence in wall-crossing formulas
• From groups to clusters
• Tame algebras have dense $\mathbf{g}$-vector fans
• Trivial Extensions of Gentle Algebras and Brauer Graph Algebras
• Acyclic cluster algebras with dense $g$-vector fans
• Derived Equivalence in Surface Algebras of Genus 0 via Graded Equivalence
• On mutations of selfinjective quivers with potential