  We algebraically analysis the quantum Hall effect of a system of particles
living on the disc ${\bf B}^1$ in the presence of an uniform magnetic field
$B$. For this, we identify the non-compact disc with the coset space
$SU(1,1)/U(1)$. This allows us to use the geometric quantization in order to
get the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitable
constraint. We show that the corresponding Hamiltonian coincides with the Maass
Laplacian. Restricting to the lowest Landau level, we introduce the
noncommutative geometry through the star product. Also we discuss the state
density behavior as well as the excitation potential of the quantum Hall
droplet. We show that the edge excitations are described by an effective
Wess-Zumino-Witten action for a strong magnetic field and discuss their nature.
We finally show that
  LLL wavefunctions are intelligent states.
