2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147631We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the representation.LaTeX2e, 9 pps. Uses amsmath & amsfonts packages. This paper is a revised version of the published article; the proof of Theorem 4 has been redone and simplifiedDifferential GeometryQuantum Physicstext