Weyl \(n\)-algebras and the Kontsevich integral of the unknot (Q2835374)

In [\textit{N. Markarian}, ``Weyl \(n\)-algebras'', Preprint, \url{arXiv:1504.01931}] the author constructed invariants of manifolds using Weyl \(n\)-algebras (a type of equivariant \(e_n\)-algebras). In the present paper the author develops this idea for manifolds and introduces the Wilson loop invariant. This invariant is connected with the Bott-Taubes invariant and the Kontsevich integral. This concept was introduced in [\textit{I. Volić}, J. Knot Theory Ramifications 16, No. 1, 1--42 (2007; Zbl 1128.57013); \textit{S. Chmutov} et al., Introduction to Vassiliev knot invariants. Cambridge: Cambridge University Press (2012; Zbl 1245.57003)]. He shows that the Wilson loop invariants of the unknot coincide with the Kontsevich integral of the unknot. The calculation of the Wilson loop invariant of the unknot in \(S^3\) is connected with a proof of the Duflo isomorphism. The author considers the Duflo isomorphism for Lie algebras with a scalar product, which is much simpler to prove than the general statement from [\textit{M. Duflo}, Ann. Sci. Éc. Norm. Supér. (4) 10, 265--288 (1977; Zbl 0353.22009)]. His construction of the Wilson loop invariant depends on the choice of a Lie algebra with a scalar product.NEWLINENEWLINEThe author explicitly calculates the first-order deformation of the differential on the Hochschild complex for the Chevalley-Eilenberg algebra of a Lie algebra. The Chevalley-Eilenberg algebra is defined in the present paper. Then he describes a construction and applies it to the quantum Chevalley-Eilenberg algebra, the role of which for perturbative Chern-Simons invariants has been explained in [Markarian, loc. cit.].