Triply special relativity

We describe an extension of special relativity characterized by three invariant scales, the speed of light c, a mass, and a length R. This is defined by a nonlinear extension of the Poincar\'e algebra A, which we describe here. For R, A becomes the Snyder presentation of the -Poincar\'e algebra, while for it becomes the phase space algebra of a particle in de Sitter spacetime. We conjecture that the algebra is relevant for the low energy behavior of quantum gravity, with taken to be the Planck mass, for the case of a nonzero cosmological constant =R^-2. We study the modifications of particle motion which follow if the algebra is taken to define the Poisson structure of the phase space of a relativistic particle.