2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105137The structure of filtered algebras of Grothendieck's differential operators of truncated polynomials in one variable and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.18 pagesAlgebraic GeometryQuantum Algebra16S32 (Primary), 16S30 (Secondary)text