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- W2070925821 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 isomorphism for algebras of chord diagrams.¶ Our main tool is a general construction of a functor from the category $ tt CycOp $ of cyclic operads to the category $ tt ModOp $ of modular operads which is left adjoint to the tree part functor $ {tt ModOp} to {tt CycOp} $ . The algebra of chord diagrams arises when this construction is applied to the operad $ {tt LIE} $ . Another example of this construction is Kontsevich's graph complex which corresponds to the operad $ {tt LIE}_infty $ for homotopy Lie algebras." @default.
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- W2070925821 date "2002-06-01" @default.
- W2070925821 modified "2023-09-29" @default.
- W2070925821 title "Cyclic operads and algebra of chord diagrams" @default.
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- W2070925821 doi "https://doi.org/10.1007/s00029-002-8106-2" @default.
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