The non-commutative Weil algebra

Details The non-commutative Weil algebra The non-commutative Weil algebra

1999-03-09

arxiv.org/abs/math/9903052v1

Invent. Math. 139 (2000), no. 1, 135--172

Mathematics

Differential Geometry

34 pages

Scientific paper

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.

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