  In this work an application of the $\kappa$--deformed algebra in condensed
matter physics is presented. Starting by the $\kappa$--deformed Dirac equation
we study the relativistic generalization of the $\kappa$--deformed Landau
levels as well as the consequences of the deformation on the Hall conductivity.
By comparing the $\kappa$--deformed Landau levels in the nonrelativistic regime
with the energy levels of a two-dimensional electron gas (2DEG) in the presence
of a normal magnetic field, upper bounds for the deformation parameter in
different materials are established. An expression for the $\kappa$--deformed
Hall conductivity of a 2DEG is obtained as well. The expression recovers the
well-known result for the usual Hall conductivity in the limit
$\varepsilon=\kappa^{-1}\to 0$. The deformation parameter breaks the Landau
levels degeneracy and due to this, it is observed that deformation gives rise
to new plateaus of conductivity in a such way that the plateaus widths of the
$\kappa$--deformed Hall conductivity are less than the usual one. By studying
the temperature dependence of the $\kappa$--deformed Hall conductivity, we show
that an increase of the temperature causes the smearing of the plateaus and a
diminution of the effect of the deformation, whilst an increase in the magnetic
field enhances the effect of the deformation.
