Projective Module Description of the q-Monopole

Abstract:

The Dirac q-monopole connection is used to compute projector matrices of quantum Hopf line bundles for arbitrary winding number. The Chern–Connes pairing of cyclic cohomology and K-theory is computed for the winding number −1. The non-triviality of this pairing is used to conclude that the quantum principal Hopf fibration is non-cleft. Among general results, we provide a left-right symmetric characterization of the canonical strong connections on quantum principal homogeneous spaces with an injective antipode. We also provide for arbitrary strong connections on algebraic quantum principal bundles (Hopf–Galois extensions) their associated covariant derivatives on projective modules.