In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.

Each Lie algebra $ℱ$ of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold $M$ définies, in a natural way, a spectral sequence $E_k\left(ℱ\right)$ which converges to the de Rham cohomology of $M$ in a finite number of steps. We prove e.g. that for all $k\ge 0$ there exists a foliated compact manifold with $E_k\left(ℱ\right)$ infinite dimensional.