Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-commutative relativistic spacetimes and worldlines from 2+1 quantum
  (anti-)de Sitter groups   The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de
Sitter groups is presented through a unified approach in which the curvature of
the spacetime (or the cosmological constant) is considered as an explicit
parameter. The Drinfel'd-double and the Poisson-Lie structure underlying the
$\kappa$-deformation are explicitly given, and the three quantum kinematical
groups are obtained as quantizations of such Poisson-Lie algebras. As a
consequence, the non-commutative (2+1)D spacetimes that generalize the
$\kappa$-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover,
noncommutative 4D spaces of (time-like) geodesics can be defined, and they can
be interpreted as a novel possibility to introduce non-commutative worldlines.
Furthermore, quantum (anti-)de Sitter algebras are presented both in the known
basis related with 2+1 quantum gravity and in a new one which generalizes the
bicrossproduct one. In this framework, the quantum deformation parameter is
related with the Planck length, and the existence of a kind of "duality"
between the cosmological constant and the Planck scale is also envisaged.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess