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The Galilean (and more generally Milne) invariance of Newtonian theory allowsfor Killing vector fields of a general kind, whereby the Lie derivative of afield is not required to vanish but only to be cancellable by someinfinitesimal Galilean (respectively Milne) gauge transformation. In thispaper, it is shown that both the Killing-Milne vector fields, which preservethe background Newtonian space-time structure, and the Killing-Cartan vectorfields, which in addition preserve the gravitational field, form a Liesubalgebra.

On the Lie subalgebra of Killing-Milne and Killing-Cartan vector fields in Newtonian space-time