Projective module description of the q-monopole

Details Projective module description of the q-monopole Projective module description of the q-monopole

1998-02-28

arxiv.org/abs/math/9803003v2

Commun.Math.Phys. 206 (1999) 247-264

Mathematics

Quantum Algebra

AMS-LaTeX 18 pages, no figures, correction of the Chern-number-sign-change Comments, 6 pages of new contents added

Scientific paper

10.1007/s002200050704

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.

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