  I introduce a reality structure on the Heisenberg double of Fun_q(SL(N,C))
for q phase, which for N=2 can be interpreted as the quantum phase space of the
particle on the q-deformed mass-hyperboloid. This construction is closely
related to the q-deformation of the symmetric top. Finally, I conjecture that
the above real form describes zero modes of certain non-compact WZNZ-models.
