It is known that the center of the universal enveloping algebra $Ug$ is isomorphic to the ring of invariant polynomials $Sg^G$ on the dual of the Lie algebra $g^*$. For $\g$ semi-simple this result is due to Harish-Chandra, and in the general case due to Duflo. If $g$ possesses a nondegenerate scalar product, the space of invariant polynomials on $g^*$ coincides with the equivariant cohomology of a point, $H_G(pt) = Sg^*_{inv} \cong Sg_{inv}$. We give a new definition of equivariant cohomology with the property $H^{new}_G(pt) = Ug_{inv}$. Equivalence of the old and new definitions implies the Duflo isomorphism. The main tool used in the proof is the Poincare Lemma stating that any closed differential form on a vector space is exact!

 
Weekly Calendar |  Mathematics Seminars |  Colloquia Schedule |  Conferences |  Calendar Archives