2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79257This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential geometry: given a smooth manifold M endowed with a flat conformal/projective structure, we establish a canonical isomorphism between the space of symmetric contravariant tensor fields on M and the space of differential operators on M. This leads to a notion of conformally/projectively invariant star-product on $T^*M$.14 pages, LaTeX; Proc. of the workshop "Noncommutative Differential Geometry and its Applications to Physics", Shonan-Kokusaimura, Japan, May 31-June 4, 1999Differential GeometryQuantum Algebratext