Quantum walks, deformed relativity, and Hopf algebra symmetries

We show how the Weyl quantum walk derived from principles in Ref. [1], enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras–the usual Poincar'e and the k-Poincar'e algebras.