  For a Lie algebra with Lie bracket got by taking commutators in a nonunital
associative algebra L, let T(L) be the vector space of tensors over L equipped
with the Ito Hopf algebra structure derived from the associative multiplication
in L. We show a necessary and sufficient condition that the double product
integral satisfy the quantum Yang-Baxter equation over T(L). We construct a
quantisation of an arbitrary quasitriangular Lie bialgebra structure on L in
the unital associative subalgebra of T(L)[[h]] consisting of formal power
series whose zero order coefficient lies in the space S(L) of symmetric
tensors.
