The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes

We derive the non-relativistic c -> infinity and ultra-relativistic c -> 0 limits of the kappa-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the kappa-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the kappa-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincare, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding kappa-Newtonian and kappa-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the kappa-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter kappa, the curvature parameter eta and the speed of light parameter c. (c) 2020 Published by Elsevier B.V.