On the Drinfeld coproduct

Abstract

This paper provides a construction of the Drinfeld coproduct $\Delta_v$ on an affine quantum Kac–Moody algebra or on a quantum affinization $\mathcal{U}$ through the exponentials of some locally nilpotent derivations, thus proving that this “coproduct” with values in a suitable completion of $\mathcal{U} \oplus \mathcal{U}$ is well defined. For the affine quantum algebras, $\Delta_v$ is also obtained as “$t$-equivariant limit” of the Drinfeld–Jimbo coproduct $\Delta$.