On coproducts of quasi-triangular Hopf algebras

We introduce two classes of coassociative comultiplications on quasi-triangular Hopf algebras. Specializing to quantum universal envelopes, these coproducts are shown to provide a universal quantization of the modified Poisson brackets on Lie groups associated with the parabolic and Iwasawa families of non-skew solutions of the modified classical Yang–Baxter equation.