Cyclic operads and algebra of chord diagrams

  title={Cyclic operads and algebra of chord diagrams},
  author={Vladimir Hinich and Arkady Vaintrob},
  journal={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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  • D. Rumynin
  • Mathematics
    Siberian Mathematical Journal
  • 2013
We study the algebras that are defined by identities in the symmetric monoidal categories; in particular, the Lie algebras. Some examples of these algebras appear in studying the knot invariants and

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