  The spin-orbit splitting of the electron levels in a two-dimensional quantum
dot in a perpendicular magnetic field is studied. It is shown that at the point
of an accidental degeneracy of the two lowest levels above the ground state the
Rashba spin-orbit coupling leads to a level anticrossing and to mixing of
spin-up and spin-down states, whereas there is no mixing of these levels due to
the Dresselhaus term. We calculate the relaxation and decoherence times of the
three lowest levels due to phonons. We find that the spin relaxation rate as a
function of a magnetic field exhibits a cusp-like structure for Rashba but not
for Dresselhaus spin-orbit interaction.
