Abstract. We prove that there is no faithful representation by skew-hermitian matrices of a ``basic algebra of observables'' ${\fb}$ on a noncompact symplectic manifold $M$. Consequently there exists no finite-dimensional quantization of {\it{any}} Lie subalgebra of the Poisson algebra $C^\infty(M)$ containing ${\fb}$.
AMSclassification. Primary 81S99; Secondary 58F06
Keywords. Quantization, Poisson algebra