  We study the symmetry properties of the Hubbard model with spin-orbit
interactions of Rashba and Dresselhaus type. These interactions break the
rotational symmetry in spin space, so that the magnetic order cannot be
excluded by using the Bogoliubov inequality method. Nevertheless, we rigorously
show that the existence of the magnetic long-range orders may be ruled out when
the Rashba and Dresselhaus coupling constants are equal in modulus, whereas the
eta-pairing can be always ruled out, regardless of the microscopic parameters
of the model. These results are obtained by imposing locally the SU(2) gauge
symmetry on the lattice, and rewriting the spin-orbit interactions in such a
way that they are included in the path ordered of the gauge field on lattice.
