Towards a topological (dual of) quantum $κ$-Poincaré group

Abstract

We argue that the $κ$-deformation is related to a factorization of a Lie group, therefore {\em an approproate version of $κ$-Poincaré does exist on the $C^*$-algebraic level}. The explict form of this factorization is computed that leads to an ``action'' of the Lorentz group (with space reflections) considered in Doubly Special Relativity theory. The orbit structure is found and ``the momentum manifold'' is extended in a way that removes singularities of the ``action'' and results in a true action. Some global properties of this manifold are investigated