Para-Galilean versus Galilean Noncommutative Phase spaces

The present paper deals with the construction of noncommutative phase spaces as coadjoint orbits of noncentral extensions of Galilei and Para-Galilei groups in two-dimensional space. The noncommutativity is due to the presence of a dual magnetic field B* in the Galilei case and of a magnetic field B in the Para-Galilei case.