  We report on the magneto-optical spectroscopy and cathodoluminescence of a
set of wurtzite (Ga,Mn)N epilayers with a low Mn content, grown by molecular
beam epitaxy. The sharpness of the absorption lines associated to the Mn$^{3+}$
internal transitions allows a precise study of its Zeeman effect in both
Faraday and Voigt configurations. We obtain a good agreement if we assume a
dynamical Jahn-Teller effect in the 3d$^{4}$ configuration of Mn, and we
determine the parameters of the effective Hamiltonians describing the
$^{5}T\_{2}$ and $^{5}E$ levels, and those of the spin Hamiltonian in the
ground spin multiplet, from which the magnetization of the isolated ion can be
calculated. On layers grown on transparent substrates, transmission close to
the band gap, and the associated magnetic circular dichroism, reveal the
presence of the giant Zeeman effect resulting from exchange interactions
between the Mn$^{3+}$ ions and the carriers. The spin-hole interaction is found
to be ferromagnetic.
