Let Ẑf be the universal Vassiliev-Kontsevich invariant for framed links in , 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 Ẑf(K(r)) = Δ(r)(Ẑf(K)), where Δ(r) is an operation of chord diagrams which replace the Wilson loop by r copies. We calculate the values of Ẑf of the Hopf links and the change of Ẑf 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.
ASJC Scopus subject areas
- Algebra and Number Theory