Address. Departement de Math\'ematiques B.P.119, Universit\'e de Tlemcen, ALGERIE
E-mail: bel@ist.cerist.dz
Abstract. Subalgebras of germs of vector fields leaving $0$ fixed in $R^{2n}$, of finite codimension in symplectic Lie algebra contain the ideal of germs infinitely flat at $0$. We give an application.
AMSclassification. 17B66
Keywords. Hamiltonian vector fields, Poisson bracket, pseudogroup action