  In this letter we study an infinite extension of the Galilei symmetry group
in any dimension that can be thought of as a non-relativistic or post-Galilean
expansion of the Poincare symmetry. We find an infinite-dimensional vector
space on which this generalized Galilei group acts and usual Minkowski space
can be modeled by our construction. We also construct particle and string
actions that are invariant under these transformations.
