# Cyclic operads and algebra of chord diagrams

@article{Hinich2000CyclicOA,
title={Cyclic operads and algebra of chord diagrams},
journal={Selecta Mathematica},
year={2000},
volume={8},
pages={237-282}
}
• Published 19 May 2000
• Mathematics
• Selecta Mathematica
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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