The fuzzy celestial sphere

We introduce a non-commutative deformation of the algebra of spherical harmonics on the celestial sphere supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on the non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.