Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory

Details Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory

1999-12-31

arxiv.org/abs/math/9912239v1

Commun. Math. Phys. 220, 301-331, 2001

Mathematics

Quantum Algebra

30 pages, LaTeX

Scientific paper

10.1007/s002200100433

We reformulate the concept of connection on a Hopf-Galois extension $B\subseteq P$ in order to apply it in computing the Chern-Connes pairing between the cyclic cohomology $HC^{2n} (B)$ and $K_0 (B)$. This reformulation allows us to show that a Hopf-Galois extension admitting a strong connection is projective and left faithfully flat. It also enables us to conclude that a strong connection is a Cuntz-Quillen-type bimodule connection. To exemplify the theory, we construct a strong connection (super Dirac monopole) to find out the Chern-Connes pairing for the super line bundles associated to super Hopf fibration.

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