K-Theoretic Hall Algebras of Quivers with Potential as Hopf Algebras

Abstract

Abstract Preprojective K-theoretic Hall algebras (KHAs), particular cases of KHAs of quivers with potential, are conjecturally positive halves of the Okounkov–Smirnov affine quantum algebras. It is thus natural to ask whether KHAs of quivers with potential are halves of a quantum group. For a symmetric quiver with potential satisfying a Künneth-type condition, we construct (positive and negative) extensions of its KHA, which are bialgebras. In particular, there are bialgebra extensions of preprojective KHAs and one can construct their Drinfeld double algebra.