  We present a different approach to the fractional quantum Hall effect (FQHE),
focusing it as a consequence of the change in the symmetry of the Hamiltonian
of every electron in a two-dimensional electron gas (2DEG) under the
application of a magnetic field and in the presence of an electrostatic
potential due to the ionized impurities, and leading to a breaking of the
degeneration of the Landau levels. As the magnetic field increases the effect
of that electrostatic potential evolves, changing in turn the spatial symmetry
of the Hamiltonian: from continuous to discrete one. The aim of both works is
to give a different picture not only of the FQHE phenomenon, but a coherent one
with the integer quantum Hall effect (IQHE) and consistent with the model
already described in Hidalgo7, 8, 9. Therefore the model gives a global view of
both effects, showing that they are aspects of the same phenomenon, and
justifying not only the appearance of the odd denominator plateaux but also the
even ones; and giving some physical reasons for the experimental fact that
there are much more odd than even denominator plateaux, hardly observed

Mesoscale and Nanoscale Physics