  Let G be a connected Lie group with Lie algebra g. The Duflo map is a vector
space isomorphism between the symmetric algebra S(g) and the universal
enveloping algebra U(g) which, as proved by Duflo, restricts to a ring
isomorphism from invariant polynomials onto the center of the universal
enveloping algebra. The Duflo map extends to a linear map from compactly
supported distributions on the Lie algebra g to compactly supported
distributions on the Lie group G, which is a ring homomorphism for G-invariant
distributions. In this paper we obtain analogues of the Duflo map and of
Duflo's theorem in the context of equivariant cohomology of G-manifolds. Our
result involves a non-commutative version of the Weil algebra and of the de
Rham model of equivariant cohomology.
