The dispersion relation for planar N = 4 supersymmetric Yang-Mills is identified with the Casimir of a quantum deformed two-dimensional kinematical symmetry, E_q(1, 1). The quantum deformed symmetry algebra is generated by the momentum, energy and boost, with deformation parameter q = e^2πi/λ. Representing the boost as the infinitesimal generator for translations on the rapidity space leads to an elliptic uniformization with crossing transformations implemented through translations by the elliptic half-periods. This quantum deformed algebra can be interpreted as the kinematical symmetry of a discrete integrable model with lattice spacing given by the BMN length a = 2π/(λ)^1/2. The interpretation of the boost generator as the corner transfer matrix is briefly discussed.