Enlarged Galilean symmetry of anyons and the Hall effect

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.