### Abstract

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.

Original language | English |
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Pages (from-to) | 271-291 |

Number of pages | 21 |

Journal | Journal of Pure and Applied Algebra |

Volume | 121 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1997 Oct 10 |

Externally published | Yes |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Le, T. T. Q., & Murakami, J. (1997). Parallel version of the universal Vassiliev-Kontsevich invariant.

*Journal of Pure and Applied Algebra*,*121*(3), 271-291. https://doi.org/10.1016/S0022-4049(96)00054-0