  The dynamic structure factor of glassy and liquid glycerol has been measured
by inelastic X-ray scattering in the exchanged momentum ($Q$) region
$Q$=2$\div$23 nm$^{-1}$ and in the temperature range 80$\div$570 K. Beside the
propagating longitudinal excitations modes, at low temperature the spectra show
a second non $Q$-dispersing peak at $\hbar \Omega_T$$\approx$8.5 meV. We assign
this peak to the transverse dynamics that, in topologically disordered systems,
acquires a longitudinal symmetry component. This assignment is substantiated by
the observation that, in the liquid, this peak vanishes when the structural
relaxation time $\tau_\alpha$ approaches $\Omega_T^{-1}$, a behavior consistent
with the condition $\tau_\alpha \Omega_T^{-1}$$>>$1 required for the existence
of a transverse-like dynamics in the liquid state.
