Symmetries of quantum spacetime in three dimensions

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant Λ, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of soq(4), with q=exp(iΛ/2κ). By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping κ finite, we obtain the kappa-Poincaré algebra of the flat quantum spacetime symmetries. © 2016 American Physical Society.