Projective module description of the q-monopole
Abstract
The quantum Hopf line bundle is constructed as a left and right projective bimodule associated to the quantum principal Hopf fibration. We prove that the covariant derivative on this bimodule that is associated to the Dirac q-monopole is a left Grassmannian connection. The Chern-Connes pairing of cyclic cohomology and K-theory is computed for the quantum Hopf line bundle revealing a purely noncommutative effect of the $K_0$-non-equivalence of the left and right projective structure. Among general results, it is shown under which conditions strong connections on algebraic quantum principal bundles (Hopf-Galois extensions) yield covariant derivatives (connections) on projective modules. We also provide a left-right symmetric characterisation of the strong canonical connections on quantum principal homogeneous spaces with an injective antipode.Keywords
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