Double product integrals and Enriquez quantisation of Lie bialgebras. II: The quantum Yang-Baxter equation (Q2571664)

This paper concerns the quantization of Lie bialgebras. After having recalled the theory of ordered double product integrals and the properties of the coproduct, the authors give a sufficient and necessary condition that a product integral satisfies the quantum Yang-Baxter equation. Next, a quantization of an arbitrary quasitriangular Lie bialgebra is constructed. The properties of the construction are also studied. Part I, cf. J. Math. Phys. 45, No. 5, 2090--2105 (2004; Zbl 1071.81073).