It is known that noncommutative fluids used to model the Fractional Quantum Hall effect give Calogero–Moser systems. The group-theoretic description of these as reductions of free motion on type A Lie algebras leads directly to Laughlin wave functions. The Calogero– Moser models also parametrise the right ideals of the Weyl algebra, which can be regarded as labelling sources in the fluid.

We show that, m the presence of a strong magnetic field, a two-dimensional interacting electron gas can eifectively be described by a Hamiltonian of'free' hard-Gore anions subject to tl~e magnetic field. According to a new understanding proposed for a set of specific anionic systems, we explain the fractional quantum Hall eifect in a very simple

Using the recently discovered Clifford statistics we propose a simple model for the grand canonical ensemble of the carriers in the theory of fractional quantum Hall effect. The model leads to a temperature limit associated with the permutational degrees of freedom of such an ensemble. We also briefly review Schur’s theory of projective representations of the permutation groups. PACS numbers: 7...