$\kappa$-de Sitter and $\kappa$-Poincar\'e 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 $\kappa$-Poincar\'e kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.