QUANTUM GROUPS, GRAVITY, AND THE GENERALIZED UNCERTAINTY PRINCIPLE

We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincare algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial-translations and rotations of the deformed Poincare algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the kappa-deformed Poincare algebra a minimal observable length emerges naturally.