  We prove dispersive and Strichartz inequalities for the solution of the wave
equation related to the full Laplacian on the Heisenberg group, by means of
Besov spaces defined by a Littlewood--Paley decomposition related to the
spectral resolution of the full Laplacian. This requires a careful analysis due
also to the non-homogeneous nature of the full Laplacian. This result has to be
compared to a previous one by Bahouri, G\'erard and Xu concerning the solution
of the wave equation related to the Kohn-Laplacian.
