Algebra, Geometry and Quantization seminar

For a finite dimensional Lie algebra g, the Duflo map S(g) rightarrow U(g) defines an isomorphism of g-modules. On g-invariant elements it gives an isomorphism of algebras. Moreover, it induces an isomorphism of algebras on the level of Lie algebra cohomology H(g,S(g)) rightarrow H(g, U(g)). However, as shown by J. Alm and S. Merkulov, it cannot be extended in a universal way to an A_infty-isomorphism between the corresponding Chevalley-Eilenberg complexes. In this talk, we will try to give an elementary and self-contained proof of this fact using a version of M. Kontsevich’s graph complex.