Interpolations between Jordanian twists, the Poincaré–Weyl algebra and dispersion relations

Abstract

We consider a two parameter family of Drinfeld twists generated from a simple Jordanian twist further twisted by 1-cochains. Twists from this family interpolate between two simple Jordanian twists. Relations between them are constructed and discussed. It is proved that there exists a one parameter family of twists identical to a simple Jordanian twist. The twisted coalgebra, star product and coordinate realizations of the κ-Minkowski noncommutative space time are presented. Real forms of Jordanian deformations are also discussed. The method of similarity transformations is applied to the Poincaré-Weyl Hopf algebra and two types of one parameter families of dispersion relations are constructed. Mathematically equivalent deformations may lead to differences in physical phenomena. * Daniel.Meljanac@irb.hr † meljanac@irb.hr ‡ zoran.skoda@uhk.cz § rina.strajn@unidu.hr

On interpolations between Jordanian twists

“…Dilatation D is included in the minimal extension of the relativistic spacetime symmetry, the so-called Poincaré-Weyl algebra, generated by {M µν , p µ , D}, where M µν denote the Lorentz generators. One parameter interpolations between Jordanian twists, generated from a simple Jordanian twist F 0 , by twisting with 1-cochains, were studied in [10,11,12,13,14].…”