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

Abstract

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 $H{C}^{2n}(B)$ 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.

30 pages, LaTeX

References in corpus (3)

• Quantum Gauge Transformations and Braided Structure on Quantum Principal Bundles
• Quantum geometry of algebra factorisations and coalgebra bundles
• Quantum differentials and the q-monopole revisited

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