  We prove that for q not a nontrivial root of unity any symmetric invariant
2-cocycle for a completion of Uq(g) is the coboundary of a central element.
Equivalently, a Drinfeld twist relating the coproducts on completions of Uq(g)
and U(g) is unique up to coboundary of a central element. As an application we
show that the spectral triple we defined in an earlier paper for the
q-deformation of a simply connected semisimple compact Lie group G does not
depend on any choices up to unitary equivalence.
