Regular Article - Theoretical Physics
Realizations of -Minkowski space, Drinfeld twists, and related symmetry algebras
Theoretical Physics Division, Ruđer Bošković Institute, Bijenička c.54, 10002, Zagreb, Croatia
* e-mail: firstname.lastname@example.org
Accepted: 25 October 2015
Published online: 5 November 2015
Realizations of -Minkowski space linear in momenta are studied for time-, space- and light-like deformations. We construct and classify all such linear realizations and express them in terms of the generators. There are three one-parameter families of linear realizations for time-like and space-like deformations, while for light-like deformations, there are only four linear realizations. The relation between a deformed Heisenberg algebra, the star product, the coproduct of momenta, and the twist operator is presented. It is proved that for each linear realization there exists a Drinfeld twist satisfying normalization and cocycle conditions. -Deformed -Hopf algebras are presented for all cases. The -Poincaré–Weyl and -Poincaré–Hopf algebras are discussed. The left–right dual -Minkowski algebra is constructed from the transposed twists. The corresponding realizations are nonlinear. All Drinfeld twists related to -Minkowski space are obtained from our construction. Finally, some physical applications are discussed.
© SIF and Springer-Verlag Berlin Heidelberg, 2015