Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant

A pure Dirac's framework for 3D Palatini's theory with cosmological constant is performed. By considering the complete phase space, we find out the full structure of the constraints, and their corresponding algebra is computed explicitly. We report that in order to obtain a well defined algebra among the constraints, the gauge group must be $SO(2,1)$. In addition, we obtain the extended action, the extended Hamiltonian, the fundamental gauge symmetry, and the Dirac brackets of the theory. Finally, we compare our results with those reported in the literature.