The noncommutative Weil algebra
Abstract
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 Ginvariant distributions. In this paper we obtain analogues of the Duflo map and of Duflo's theorem in the context of equivariant cohomology of Gmanifolds. Our result involves a noncommutative version of the Weil algebra and of the de Rham model of equivariant cohomology.
 Publication:

Inventiones Mathematicae
 Pub Date:
 January 2000
 DOI:
 10.1007/s002229900025
 arXiv:
 arXiv:math/9903052
 Bibcode:
 2000InMat.139..135A
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 34 pages