Nearly Morita equivalence for neighboring Jacobian algebras

David Smith

Quivers with potentials were recently introduced by Derksen, Weyman and Zelevinsky. In their paper, they define a mutation procedure for quivers with potentials, and further for their associated Jacobian algebras. In this talk, we discuss these objects and show that if a Jacobian algebra A is mutated into an algebra B, then their categories of finite dimensional modules are nearly Morita equivalent. This generalizes analogue results for cluster-tilted algebras and 2-CY-tilted algebras. This is part of a join work with A. Buan, O. Iyama and I. Reiten.