The inclusion of the cosmological constant is one of the main questions faced by quantum gravity. In three dimensions, non-perturbative approaches to quantum gravity including loop quantum gravity (LQG), combinatorial quantization and spinfoam path integrals encode the cosmological constant as a deformation parameter in a quantum group structure. In this talk, I will focus on the LQG approach: I will explain the Poisson-Lie structure of the classical phase space and how its quantization naturally leads to the emergence of quantum groups. I will use the holonomy-ﬂux algebra and its spinorial presentation introduced in the series of work by Bonzom, Dupuis, Girelli, Livine and myself. This allows to construct the Hamiltonian constraint, understand its matrix elements as Turaev-Viro amplitudes. This connects LQG to the other approaches in a uniﬁed mathematical setting.
- Quantum Gravity
- Scientific Series