  We discuss the proof of Kazhdan and Lusztig of the equivalence of the
Drinfeld category D(g,h) of g-modules and the category of finite dimensional
Uq(g)-modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists the
result is formulated as the existence for each h\in iR of a normalized unitary
2-cochain F on the dual \hat G of a compact simple Lie group G such that the
convolution algebra of G with the coproduct twisted by F is *-isomorphic to the
convolution algebra of the q-deformation G_q of G, while the coboundary of
F^{-1} coincides with Drinfeld's KZ-associator defined via monodromy of the
Knizhnik-Zamolodchikov equations.
