Representations of the Lie algebra of the homogeneous Galilei group and their relation to the representations of the Lorentz algebra

The irreducible Hermitian representations of the Lie algebra of the homogeneous Galilei group were first constructed by using the method of the maximal compact subgroup. The same representations were then obtained by contracting the irreducible representations of the homogeneous Lorentz group. In the Appendix, the faithful representations are given with the diagonalized generators of the velocity transformations.