Vassiliev knot invariants and lie $S$-algebras

The goal of this work is to explain the appearance of Lie algebras in the theory of knot invariants of finite order (\Vas\ invariants). As a byproduct, we find a new construction of such invariants. Namely, we show that the theory of \Vas\ invariants leads naturally to the notion of $S$-Lie algebra, where $S$ is an involutive solution of the \QYBE. For each $S$-Lie algebra $L$ with an $L$-invariant $S$-symmetric non-degenerate bilinear form $b$ and an invariant functional on its universal enveloping algebra, we construct a sequence of \Vas\ \ki s.

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Published 1 January 1994