A note on the geometrical interpretation of quantum groups and   non-commutative spaces in gravity
  Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\sqrt{Lambda} related the cosmological constant Lambda. This yields a simple geometrical interpretation for the relation between the quantum deformation parameter q=exp[i Lambda l_{Planck}^2 ] and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces. 
Eugenio Bianchi and Carlo Rovelli
gr-qc hep-th