A Frobenius manifold for $$\ell $$-Kronecker quiver

Abstract

We construct a Frobenius structure whose intersection form coincides with the generalized Cartan matrix of the \(\ell \)-Kronecker quiver \(K_{\ell }\), and underlying complex manifold is isomorphic to the space of stability conditions for the bounded derived category of finitely generated modules over the path algebra \({{\mathbb {C}}}K_{\ell }\).