The quantum Poincare group from quantum group contraction

Abstract

We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$ is sent to one. The bicrossproduct structure of the quantum Poincaré group is exhibited and shown to be dual to the one of the $κ$--Poincaré Hopf algebra, at least in two dimensions.