The κ(A)dS quantum algebra in (3 + 1) dimensions
Abstract
The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ(A)dS quantum algebra in (3 + 1) dimensions as the corresponding PoissonLie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a PoissonLie group contraction parameter, and the limit Λ → 0 leads to the wellknown κPoincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ(A)dS deformation is sketched.
 Publication:

Physics Letters B
 Pub Date:
 March 2017
 DOI:
 10.1016/j.physletb.2017.01.020
 arXiv:
 arXiv:1612.03169
 Bibcode:
 2017PhLB..766..205B
 Keywords:

 Antide Sitter;
 Cosmological constant;
 Quantum groups;
 PoissonLie groups;
 Lie bialgebras;
 Quantum duality principle;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 13 pages