Quantum (anti)de Sitter algebras and generalizations of the kappa-Minkowski space

TL;DR

This paper introduces two quantum deformations of (anti)de Sitter algebras, leading to new non-commutative spacetimes that generalize kappa-Minkowski space, with potential implications for quantum gravity and spacetime structure.

Contribution

It presents novel non-standard and standard quantum deformations of (anti)de Sitter algebras and constructs associated non-commutative spacetimes, extending the kappa-Minkowski framework.

Findings

Two distinct quantum deformations of (anti)de Sitter algebras are constructed.

New non-commutative spacetimes generalizing kappa-Minkowski are proposed.

Deformation parameters relate to Planck length and cosmological constant.

Abstract

We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while the latter is a standard (quasitriangular) deformation of both SO(2,2) and SO(3,1) expressed as the kinematical groups of the (2+1)D anti-de Sitter and de Sitter spacetimes, respectively. The Hopf structure of the quantum algebra and a study of the dual quantum group are presented for each deformation. These results enable us to propose new non-commutative spacetimes that can be interpreted as generalizations of the kappa-Minkowski space, either by considering a variable deformation parameter (depending on the boost coordinates) in the conformal deformation, or by introducing an explicit curvature/cosmological constant in the kinematical one; kappa-Minkowski turns out to be the common first-order structure for all of these quantum spaces. Some properties provided by these deformations, such as dimensions of the deformation parameter (related with the Planck length), space isotropy, deformed boost transformations, etc., are also commented.