  We show that the integer quantum Hall effect systems in plane, sphere or
disc, can be formulated in terms of an algebraic unified scheme. This can be
achieved by making use of a generalized Weyl--Heisenberg algebra and
investigating its basic features. We study the electromagnetic excitation and
derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann
space (phase space). This excitation is introduced through a deformation
(perturbation) of the symplectic structure of the phase space. We show the
major role of Moser's lemma in dressing procedure, which allows us to eliminate
the fluctuations of the symplectic structure. We discuss the emergence of the
Seiberg--Witten map and generation of an abelian noncommutative gauge field in
the theory. As illustration of our model, we give the action describing the
electromagnetic excitation of a quantum Hall droplet in two-dimensional
manifold.
