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# Mathematical Research Letters

## Volume 1 (1994)

### Number 5

### Vassiliev knot invariants and lie $S$-algebras

Pages: 579 – 595

DOI: http://dx.doi.org/10.4310/MRL.1994.v1.n5.a6

#### Author

#### Abstract

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.