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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 theparticle on the q-deformed mass-hyperboloid. This construction is closelyrelated to the q-deformation of the symmetric top. Finally, I conjecture thatthe above real form describes zero modes of certain non-compact WZNZ-models.Comment: 12 pages, LaTeX, no figure

QUANTUM ALGEBRA OF THE PARTICLE MOVING ON THE q-DEFORMED MASS-HYPERBOLOID