Cohomological Hall algebras and affine quantum groups

We study the preprojective cohomological Hall algebra (CoHA) introduced by the authors in Yang and Zhao (The cohomological Hall algebra of a preprojective algebra. <, 2015) for any quiver Q and any one-parameter formal group . In this paper, we construct a comultiplication on the CoHA, making it a bialgebra. We also construct the Drinfeld double of the CoHA. The Drinfeld double is a quantum affine algebra of the Lie algebra associated to Q, whose quantization comes from the formal group . We prove, when the group is the additive group, the Drinfeld double of the CoHA is isomorphic to the Yangian.