On the fractional quantum hall effect

We show in the Hartree-Fock approximation that the formation of a two dimensional electron lattice allows for a natural explanation of the anomalous fractional quantum Hall effect. Landau levels are broadened and split in a number of bands in such a way that if the number of electrons per unit cell is a half odd integer the Fermi energy is in a gap for an odd filling fraction denominator, and at the center of a band if the denominator is even.