Symmetries of quantum spacetime in three dimensions
Symmetries of quantum spacetime in three dimensions
By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\mathrm{\ensuremath{\Lambda}}$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of ${\mathfrak{so}}_{q}(4)$, with $q=\mathrm{exp}(i\ensuremath{\hbar}\sqrt{\mathrm{\ensuremath{\Lambda}}}/2\ensuremath{\kappa})$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, …