K-theoretic Hall algebras of quivers with potential as Hopf algebras

TL;DR

This paper constructs bialgebra extensions of K-theoretic Hall algebras for symmetric quivers with potential, enabling the formation of their Drinfeld doubles, thus advancing algebraic structures in representation theory.

Contribution

It introduces new bialgebra extensions of K-theoretic Hall algebras for symmetric quivers with potential, including their Drinfeld doubles, under a K"unneth-type condition.

Findings

Bialgebra extensions of K-theoretic Hall algebras constructed

Drinfeld double algebra of these extensions built

Applicable to preprojective K-theoretic Hall algebras

Abstract

For $(Q,W)$ a symmetric quiver with potential satisfying a K\"unneth-type condition, we construct (positive and negative) extensions of its K-theoretic Hall algebra which are bialgebras. In particular, there are bialgebra extensions of preprojective KHAs of a quiver $Q$ and one can construct their Drinfeld double algebra.