MOYAL QUANTIZATION OF 2 + 1-DIMENSIONAL GALILEAN SYSTEMS

Stratonovich-Weyl kernels are constructed for some of the coadjoint orbits of the two-dimensional extended Galilean group G (2 + 1)BAR. As an intermediate step, the unitary irreducible representations associated with a given group orbit are obtained by using the Kirillov-Mackey theory. Star products are defined, in the sense of Moyal, for functions on each of these orbits. The central extension of G (2 + 1) with parameter k is also analyzed, which results from the commutator between the generators of boosts, to conclude that it originates a sort of nonrelativistic remainder of the Thomas precession.