Paper detail

Weyl n-algebras and the Kontsevich integral of the unknot

Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a $dg$-scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the first section we explicitly calculate the first order deformation of the differential on the Hochschild complex of the Chevalley--Eilenberg algebra. The answer contains the Duflo character. This calculation is used in the last section. There we sketch the definition of the Wilson loop invariant of knots, which is hopefully equal to the Kontsevich integral, and show that for unknot they coincide. As a byproduct we get a new proof of the Duflo isomorphism for a Lie algebra with a scalar product.