S. Majid et H. Ruegg, BICROSSPRODUCT STRUCTURE OF KAPPA-POINCARE GROUP AND NONCOMMUTATIVE GEOMETRY, Physics letters. Section B, 334(3-4), 1994, pp. 348-354
We show that the kappa-deformed Poincare quantum algebra proposed for
elementary particle physics has the structure of a Hopf algebra bicros
sproduct U(so(1,3)) T. The algebra is a semidirect product of the clas
sical Lorentz group so(1,3) acting in a deformed way on the momentum s
ector T. The novel feature is that the coalgebra is also semidirect, w
ith a backreaction of the momentum sector on the Lorentz rotations. Us
ing this, we show that the kappa-Poincare acts covariantly on a kappa-
Minkowski space, which we introduce. It turns out necessarily to be de
formed and non-commutative. We also connect this algebra with a previo
us approach to Planck scale physics.