The pauli principle for a quantum theory on T2 with magnetic field

We discuss the reducible representation of n particles on a torus with magnetic field, where the gauge automorphisms are unitarily implementable. This representation is of type II∞, if B is not integer. We show that there is a natural splitting into I∞ ⊗ II1 such that the Pauli exclusion principle acts only in the first factor. Under this condition we estimate the ground state energy for several particles and show that in the thermodynamic limit we obtain the correct result.