  We construct free Lie algebras which, together with the algebra of spatial
rotations, form infinite-dimensional extensions of finite-dimensional Galilei
Maxwell algebras appearing as global spacetime symmetries of extended
non-relativistic objects and non-relativistic gravity theories. We show how
various extensions of the ordinary Galilei algebra can be obtained by
truncations and contractions, in some cases via an affine Kac-Moody algebra.
The infinite-dimensional Lie algebras could be useful in the construction of
generalized Newton-Cartan theories gravity theories and the objects that couple
to them.
