ABSTRACT
Galilei symmetry is the symmetry of nonrelativistic spacetime. It corresponds to the maximally admissible set of transformations between Galileian inertial reference frames. Beyond this global definition, it is enlightening to construct the Galilei group G step by step from the ground up. The relativistic Lorentz group consists of linear transformations from the outset, and it acts on a 4-dimensional spacetime. Poincare transformations, which are affine-linear, are rendered linear by considering them in one additional dimension. Conformal transformations are nonlinear, but remarkably, they can also be made linear by adding two additional dimensions. The Galilei transformations are typically treated in books on classical mechanics and quantum mechanics.
