THE ALGEBRAIC STRUCTURE OF THE GENERALIZED UNCERTAINTY PRINCIPLE

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter kappa is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in DELTAp/M(PL). We also briefly comment on possible implications for Lorentz invariance at the Planck scale.