# Cyclic operads and algebra of chord diagrams

@article{Hinich2000CyclicOA, title={Cyclic operads and algebra of chord diagrams}, author={Vladimir Hinich and Arkady Vaintrob}, journal={Selecta Mathematica}, year={2000}, volume={8}, pages={237-282} }

Abstract. We prove that the algebra
$ \cal A $ of chord diagrams, the dual to the associated graded algebra of Vassiliev knot invariants, is isomorphic to the universal enveloping algebra of a Casimir Lie algebra in a certain tensor category (the PROP for Casimir Lie algebras). This puts on a firm ground a known statement that the algebra
$ \cal A $ "looks and behaves like a universal enveloping algebra". An immediate corollary of our result is the conjecture of [BGRT] on the Kirillov-Duflo…

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