# The κ-(A)dS quantum algebra in (3 + 1) dimensions

@article{Ballesteros2016TheQ,
title={The $\kappa$-(A)dS quantum algebra in (3 + 1) dimensions},
author={{\'A}ngel Ballesteros and Francisco J. Herranz and Fabio Musso and Pedro Naranjo},
journal={Physics Letters B},
year={2016},
volume={766},
pages={205-211}
}
• Published 9 December 2016
• Mathematics
• Physics Letters B
21 Citations
• Physics, Mathematics
Physics Letters B
• 2019
• Mathematics
Classical and Quantum Gravity
• 2021
The complete classification of classical r-matrices generating quantum deformations of the (3 + 1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum subgroup is
• Physics
• 2019
The (3+1)-dimensional κ-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the κ-(A)dS Poisson homogeneous space. Under minimal physical
• Mathematics, Physics
Physical Review D
• 2018
Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated
• Physics
Symmetry
• 2021
The properties and relations of these algebras of relativistic symmetries and their associated noncommutative spacetimes are surveyed, emphasizing the nontrivial effects of interplay between curvature, quantum deformation and speed of light parameters.
• Mathematics
Classical and Quantum Gravity
• 2018
The eight nonisomorphic Drinfel’d double (DD) structures for the Poincaré Lie group in (2  +  1) dimensions are explicitly constructed in the kinematical basis. Also, the two existing DD structures

## References

SHOWING 1-10 OF 80 REFERENCES

• Mathematics
• 2014
Quantum deformations of (anti-)de Sitter (A)dS algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of
• Mathematics
• 1994
In this paper we give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describes all groups of motions of classical geometries in N=3
• Mathematics
• 2013
A systematic computational approach for the explicit construction of any quantum Hopf algebra (Uz(g), Δz) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the
• Mathematics
• 1993
A global model of the q deformation for the quasiorthogonal Lie algebras generating the groups of motions of the four‐dimensional affine Cayley–Klein (CK) geometries is obtained starting from the