2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114138We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural operations to the study of polynomial maps between (vector) spaces of jets which are equivariant with respect to certain algebraic groups. Using the IT-reduction, we obtain short and conceptual proofs of some known results on the classification of certain natural operations (the Schouten theorem, etc) together with new results including the non-existence of a universal deformation quantization on Poisson manifolds.AmSLaTeX, 22 pages, 23 bibliography itemsDifferential GeometryAlgebraic Geometry53A55 (Primary); 58A20, 58A32, 53D55 (Secondary)text