Strong Connections and Chern–Connes Pairing¶in the Hopf–Galois Theory
- Cite this article as:
- Dąbrowski, L., Grosse, H. & Hajac, M. Commun. Math. Phys. (2001) 220: 301. doi:10.1007/s002200100433
We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC2n (B) and K0 (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 a super Hopf fibration.
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