Parallel version of the universal Vassiliev-Kontsevich invariant

Let Ẑ_f be the universal Vassiliev-Kontsevich invariant for framed links in [13], which is a generalization of Kontsevich's invariant in [10, 1]. Let K be a framed knot and K^(r) be its r-parallel. Then we show Ẑ_f(K^(r)) = Δ_(r)(Ẑ_f(K)), where Δ_(r) is an operation of chord diagrams which replace the Wilson loop by r copies. We calculate the values of Ẑ_f of the Hopf links and the change of Ẑ_f under the Kirby moves. An explicit formula of an important normalization factor, which is the value of the trivial knot, in the universal enveloping algebra U(g) of any Lie algebra is given.