  We consider two ways of introducing minimal Abelian gauge interactions into
the model presented in [1]. They are different only if the second central
charge of the planar Galilei group is nonzero. One way leads to standard gauge
transformations and second to a generalized gauge theory with gauge
transformations accompanied by time-dependent area-preserving coordinate
transformations. Both approaches, however, are related to each other by a
classical Seiberg-Witten map supplemented by the noncanonical transformation of
the phase space variables for planar particles. We also formulate the two-body
problem in the model with a generalized gauge symmetry and consider the case
with both CS and background electromagnetic fields, as it is used in the
description of fractional quantum Hall effect.
