Quantum groups and q-lattices in space

Quantum groups put physics on a q-lattice. We shall see that this q-deformed phase space can be imbedded in an ordinary quantum mechanical phase space and that q-deformation has many similarities with a spontaneous breaking of a continuous spectrum to a discrete spectrum (continuous space to lattice). The first step will be to base the q-deformed phase space on a non-commutative differential structure compatible with the non-commutative configuration space and the quantum group symmetry. In the next step we have to define conjugation properties on the non-commutative algebraic system that can be identified with hermitean conjugation of the corresponding operators in Hilbert space