  We use the method of invariants to derive one- and two-band effective
Hamiltonians of a noncentrosymmetric two-dimensional electron gas, in the
presence of magnetic field. A complete classification of the antisymmetric
spin-orbit and magnetic coupling terms near the $\Gamma$ point is developed for
all two-dimensional crystal symmetries. The effective Hamiltonian depends on
the symmetry of the Bloch bands at the $\Gamma$ point, which is described by
one of the double-valued corepresentations of the two-dimensional magnetic
point group. In some bands, the spin-orbit coupling is cubic in the electron
momentum and the effective Zeeman interaction is strongly anisotropic. As an
example of a two-band effective Hamiltonian, we introduce a simple model of a
topological insulator with the intraband and interband spin-orbit coupling and
investigate its bulk and boundary properties.
