Noncommutative geometry of angular momentum space U(su(2))

We study the standard angular momentum algebra [x_i,x_j]=ıλɛ_ijkx_k as a noncommutative manifold Rλ3. We show that there is a natural 4D differential calculus and obtain its cohomology and Hodge ^* operator. We solve the spin 0 wave equation and some aspects of the Maxwell or electromagnetic theory including solutions for a uniform electric current density, and we find a natural Dirac operator ∂/. We embed Rλ3 inside a 4D noncommutative space-time which is the limit q→1 of q-Minkowski space and show that Rλ3 has a natural quantum isometry group given by the quantum double C₍^{SU(2))⋊U(su(2)) which is a singular limit of the q-Lorentz group. We view Rλ3} as a collection of all fuzzy spheres taken together. We also analyze the semiclassical limit via minimum uncertainty states |j,θ,φ> approximating classical positions in polar coordinates.