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We algebraically analysis the quantum Hall effect of a system of particlesliving 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 toget the wavefunctions as the Wigner ${\cal D}$-functions satisfying a suitableconstraint. We show that the corresponding Hamiltonian coincides with the MaassLaplacian. Restricting to the lowest Landau level, we introduce thenoncommutative geometry through the star product. Also we discuss the statedensity behavior as well as the excitation potential of the quantum Halldroplet. We show that the edge excitations are described by an effectiveWess-Zumino-Witten action for a strong magnetic field and discuss their nature.We finally show that  LLL wavefunctions are intelligent states.Comment: 18 pages, clarifications and misprints corrected, version published  in IJGMM

QUANTUM HALL DROPLETS ON DISC AND EFFECTIVE WESS–ZUMINO–WITTEN ACTION FOR EDGE STATES