Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD behaviour, both with and without feedback of the magnetic field on the flow. These results are expected to be useful for the solution of MHD equations in both tokamak fusion experiments and space plasmas.
