The non-commutative Weil algebra

For any compact Lie group G, together with an invariant inner product on it s Lie algebra g, we define the non-commutative Well algebra W-G; as a tenso r product of the universal enveloping algebra U(g) and the Clifford algebra Cl(8). Just like the usual Well algebra W-G = S(g*) x boolean AND g*, W-G carries the structure of an acyclic, locally free G-differential algebra an d can be used to define equivariant cohomology H-G(B) for any G-differentia l algebra B. We construct an explicit isomorphism Q : N-G --> W-G Of the tw o Well algebras as G-differential spaces, and prove that their multiplicati on maps are G-chain homotopic. This implies that the map in cohomology H-G( B) --> H-G(B) induced by Q is a ring isomorphism. For the trivial G-differe ntial algebra B = R, this reduces to the Duflo isomorphism S(g)(G) congruen t to U(g)(G) between the ring of invariant polynomials and the ring of Casi mir elements.