A note on the Chevalley-Eilenberg cohomology for the Galilei and Poincare algebras

We construct in a systematic way the complete Chevalley-Eilenberg cohomology at form degrees 2, 3 and 4 for the Galilei and Poincare groups. The corresponding non-trivial forms belong to certain representations of the spatial rotation (Lorentz) group. In the case of 2-forms they give all possible central and non-central extensions of the Galilei group (and all non-central extensions of the Poincare group). The procedure developed in this paper can be applied to any spacetime symmetry group.