Bicrossproduct structure of κPoincare group and noncommutative geometry
Abstract
We show that the κdeformed Poincaré quantum algebra proposed for 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 formed 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 κPoincare acts covariantly on a κMinkowski space, which we introduce. It turns out necessarily to be deformed and noncommutative. We also connect this algebra with a previous approach to Planck scale physics.
 Publication:

Physics Letters B
 Pub Date:
 August 1994
 DOI:
 10.1016/03702693(94)906998
 arXiv:
 arXiv:hepth/9405107
 Bibcode:
 1994PhLB..334..348M
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 12 pages. Revision: minor typos corrected