K-theoretic Hall algebras, quantum groups and super quantum groups

We prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group. We also compare super toroidal quantum groups of type A with some K-theoretic Hall algebras of quivers with potential introduced recently by Padurariu using categories of singularities of some Landau–Ginzburg models. The proof uses both a deformation of the K-theoretic Hall algebra and a dimensional reduction which allows us to compare the KHA of preprojective algebras to the K-theoretic Hall algebras of a quiver with potential.