2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58507We present explicit formulas for deformation quantization on the co-adjoint orbits of the real diamond Lie group. From this we obtain quantum half-plans, quantum hyperbolic cylinders, quantum hyperbolic paraboloids via Fedosov deformation quantization and finally, the corresponding unitary representations of this group.13 AmS-LaTeX file, no figureQuantum AlgebraRepresentation Theorytext