$\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant

Abstract

Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $\kappa$-de Sitter and, in the vanishing cosmological limit, of $\kappa$-Poincaré kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.

This is an improved version after the journal reviewing process

References in corpus (5)

• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Deformed Carroll particle from 2+1 gravity

Cited by in corpus (2)

• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei