Deformations of the Galilean algebra

All the infinitesimal deformations of the Galilean algebra with and without central extension are computed, as well as their integrability properties. Among the four-parameter family of infinitesimal deformations of the unextended algebra is found the Newton algebras, the Euclidean algebra E(4), the Poincaré algebra, the de Sitter algebras, and SO(5). For the centrally extended algebra there is found, in particular, an infinitesimal deformation containing a Poincaré subalgebra (although the embedding is not the natural one), and centrally extended versions of the Newton algebras.