Communications in Mathematical Physics

, Volume 220, Issue 2, pp 301–331

Strong Connections and Chern–Connes Pairing¶in the Hopf–Galois Theory

  • Ludwik Dąbrowski
  • Harald Grosse
  • M. Hajac

DOI: 10.1007/s002200100433

Cite this article as:
Dąbrowski, L., Grosse, H. & Hajac, M. Commun. Math. Phys. (2001) 220: 301. doi:10.1007/s002200100433

Abstract:

We reformulate the concept of connection on a Hopf–Galois extension BP 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ludwik Dąbrowski
    • 1
  • Harald Grosse
    • 2
  • M. Hajac
    • 3
  1. 1.Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2–4, 34014 Trieste, Italy.¶E-mail: dabrow@sissa.itIT
  2. 2.Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.¶E-mail: grosse@thp.univie.ac.atAT
  3. 3.Mathematical Institute, Polish Academy of Sciences, ul. Śniadeckich 8, Warsaw, 00-950, PolandPL
  4. 4.Department of Mathematical Methods in Physics, Warsaw University, ul. Hoża 74, Warsaw, 00-682, Poland.¶E-mail: pmh@fuw.edu.plPL

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