On the Lie subalgebra of Killing-Milne and Killing-Cartan vector fields   in Newtonian space-time
  The Galilean (and more generally Milne) invariance of Newtonian theory allows for Killing vector fields of a general kind, whereby the Lie derivative of a field is not required to vanish but only to be cancellable by some infinitesimal Galilean (respectively Milne) gauge transformation. In this paper, it is shown that both the Killing-Milne vector fields, which preserve the background Newtonian space-time structure, and the Killing-Cartan vector fields, which in addition preserve the gravitational field, form a Lie subalgebra. 
N. Chamel
gr-qc math-ph math.MP