W-Infinity Algebras from Noncommutative Chern-Simons Theory
  We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_\infty$ algebra. The deformation depends on the level (the coefficient in the Chern-Simons action), and the noncommutativity parameter, which were identified, respectively, with the inverse filling fraction and the inverse density in a recent description of the fractional quantum Hall effect. We remark on the quantization of our algebra. The results are sensitive to the choice of ordering in the Gauss law. 
A. Pinzul and A. Stern