  We study the effect of electron-electron interaction and spin on electronic
and transport properties of gated graphene nanoribbons (GNRs) in a
perpendicular magnetic field in the regime of the lowest Landau level (LL). The
electron-electron interaction is taken into account using the Hartree and
Hubbard approximations, and the conductance of GNRs is calculated on the basis
of the recursive Greens function technique within the Landauer formalism. We
demonstrate that, in comparison to the one-electron picture, electron-electron
interaction leads to the drastic changes in the dispersion relation and
structure of propagating states in the regime of the lowest LL showing a
formation of the compressible strip and opening of additional conductive
channels in the middle of the ribbon. We show that the latter are very
sensitive to disorder and get scattered even if the concentration of disorder
is moderate. In contrast, the edge states transport is very robust and can not
be suppressed even in the presence of a strong spin-flipping.
