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

Abstract

We argue that the $\kappa$-deformation is related to a factorization of a Lie group, therefore {\em an approproate version of $\kappa$-Poincaré does exist on the $C^{\ast }$-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

Latex, 22 pages, uspackage: pstricks,pst-plot

References in corpus (3)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Deformed Boost Transformations That Saturate at the Planck Scale

Cited by in corpus (2)

• Classical basis for kappa-Poincare algebra and doubly special relativity theories
• Semidirect products of C*-quantum groups: multiplicative unitaries approach