Projectively Equivariant Quantization Map

Abstract

Let M be a manifold endowed with a symmetric affine connection $\Gamma .$ The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T^{*} M and the space of second-order linear differential operators, both viewed as modules over the group of diffeomorphisms and the Lie algebra of vector fields on M. This map is an isomorphism, for almost all values of certain constants, and it depend only on the projective class of the affine connection $\Gamma .$

The results of this paper have been surpassed by several results. The title has been corrected to avoid wrong citations

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• On osp(p+1,q+1|2r)-equivariant quantizations
• Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold