  A physically relevant unitary irreducible non-projective representation of
the Galilei group is possible in the Koopman-von Neumann formulation of
classical mechanics. This classical representation is characterized by the
vanishing of the central charge of the Galilei algebra. This is in contrast to
the quantum case where the mass plays the role of the central charge. Here we
show, by direct construction, that classical mechanics also allows for a
projective representation of the Galilei group where the mass is the central
charge of the algebra. We extend the result to certain kind of
quantum-classical hybrid systems.
