A fuzzy bipolar celestial sphere

We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics 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 such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.