Vassiliev knot invariants and lie $S$-algebras
Arkady Vaintro · Mathematical Research Letters · 1994
The goal of this work is to explain the appearance of Lie algebras in the theory of knot invariants of finite order (Vassiliev invariants).As a byproduct, we find a new construction of such invariants.Namely, we show that the theory of Vassiliev invariants leads naturally to the notion of S-Lie algebra, where S is an involutive solution of the quantum Yang-Baxter equation.For each S-Lie algebra L with an L-invariant Ssymmetric non-degenerate bilinear form b and an invariant functional on its universal enveloping algebra, we construct a sequence of Vassiliev knot invariants.