Quantum groups and noncommutative spacetimes with cosmological constant

Abstract

Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum groups is reviewed. In this approach the quantum deformation parameter $z$ is related to a Planck scale, and the cosmological constant $\Lambda$ plays the role of a second deformation parameter of geometric nature, whose limit $\Lambda \to 0$ provides the corresponding noncommutative Minkowski spacetimes.

10 pages. Based on the contribution presented at "Eighth International Workshop DICE2016", Castello Pasquini in Castiglioncello, Italy, September 12-16, 2016

References in corpus (22)

• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Modern tests of Lorentz invariance
• Quantum Spacetime Phenomenology
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
• Covariant Non-Commutative Space-Time
• IceCube and GRB neutrinos propagating in quantum spacetime
• Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
• Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter
• A non-commutative Minkowskian spacetime from a quantum AdS algebra
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• Drinfel'd doubles for (2+1)-gravity
• Kinematics of particles with quantum de Sitter symmetries
• On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions
• A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

Cited by in corpus (3)

• The Poincaré group as a Drinfel'd double
• Drinfel'd double structures for Poincaré and Euclidean groups
• Curving Flat Space-Time by Deformation Quantization?