Narrow Results

We describe how to reduce the fuzzy four-sphere algebra to a set of four independent raising and lowering oscillator operators. In terms of them we derive the projector valued operators for the fuzzy four-sphere, which are the global definition of k-instanton connections over this noncommutative base manifold.

We deconstruct the finite projective modules for the fuzzy four-sphere, described in a previous paper, and correlate them with the matrix model approach, making manifest the physical implications of noncommutative topology. We briefly discuss also the U(2) case, being a smooth deformation of the celebrated BPST SU(2) classical instantons on a sphere.