Vassiliev knot invariants and lie $S$-algebras

@article{Vaintro1994VassilievKI,
  title={Vassiliev knot invariants and lie \$S\$-algebras},
  author={Arkady Vaintro},
  journal={Mathematical Research Letters},
  year={1994},
  volume={1},
  pages={579-595}
}
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… Expand
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