BICROSSPRODUCT STRUCTURE OF KAPPA-POINCARE GROUP AND NONCOMMUTATIVE GEOMETRY

We show that the kappa-deformed Poincare quantum algebra proposed for elementary particle physics has the structure of a Hopf algebra bicrossproduct U(so(1,3)) T. The algebra is a semidirect product of the classical Lorentz group so(1,3) acting in a deformed way on the momentum sector T. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the kappa-Poincare acts covariantly on a kappa-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.