In the last few years, various knot invariants have been discovered. At present, Vassiliev knot invariants are the strongest among all known ones, see, e.g., The essential notion in Vassiliev's theory is the notion of chord diagram. Chord diagrams have an interesting algebraic structure. It turns out that this structure is deeply connected with Lie-algebra representations. In his article, D. Bar-Natan shows the way to construct invariant tensors for the adjoint action on semisimple Lie algebra tensors by using chord diagrams.
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机译：在最近几年中，已经发现了各种结不变式。目前，Vassiliev结不变量是所有已知的最强，例如，参见Vassiliev理论中的基本概念是和弦图。和弦图具有有趣的代数结构。事实证明，这种结构与李代数表示法密切相关。 D. Bar-Natan在他的文章中展示了使用弦图为半简单李代数张量上的伴随动作构造不变张量的方法。
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