  Enlarged planar Galilean symmetry, built of both space-time and field
variables and also incorporating the ``exotic'' central extension is
introduced. It is used to describe non-relativistic anyons coupled to an
electromagnetic field. Our theory exhibits an anomalous velocity relation of
the type used to explain the Anomalous Hall Effect. The Hall motions,
characterized by a Casimir of the enlarged algebra, become mandatory for some
critical value(s) of the magnetic field. The extension of our scheme yields the
semiclassical effective model of the Bloch electron.
