Genteelness conjecture for Jacobian algebras of generic quivers with potential

Let (Q,W)(Q,W) be a quiver with a generic potential, and suppose that its Jacobian algebra J(Q,W)J_{(Q,W)} is finite dimensional. Genteelness conjecture. The Jacobian algebra J(Q,W)J_{(Q,W)} is genteel. Here a generic potential means a generic point in the space of all potentials in the sense attributed to Derksen, Weyman, and Zelevinsky; in particular, it is non-degenerate. This conjecture proposes that finite-dimensional Jacobian algebras arising from generic quivers with potential satisfy the representation-theoretic condition of weak genteelness; no resolution is given in the source.

Sources & referencesView supporting material

Primary source

Fan Qin, “Bases for upper cluster algebras and tropical points”, arXiv:1902.09507 (2021).

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