  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.
