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

Arkady Vaintro (New Mexico State University)

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.

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