Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory
Copyright policy )Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory
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.
30 pages, LaTeX
- Polish Academy of Learning Poland
- Universität Wien Austria
- University of Vienna Austria
- Institute for Theoretical Physics Switzerland
- Universität Wien
Noncommutative geometry (à la Connes), 103036 Theoretische Physik, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, strong connection, K-Theory and Homology (math.KT), Mathematical Physics (math-ph), Chern-Connes pairing, Hopf algebras (associative rings and algebras), Hopf-Galois theory, 103036 Theoretical physics, Mathematics - Quantum Algebra, Mathematics - K-Theory and Homology, FOS: Mathematics, Quantum Algebra (math.QA), Mathematical Physics
Noncommutative geometry (à la Connes), 103036 Theoretische Physik, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, strong connection, K-Theory and Homology (math.KT), Mathematical Physics (math-ph), Chern-Connes pairing, Hopf algebras (associative rings and algebras), Hopf-Galois theory, 103036 Theoretical physics, Mathematics - Quantum Algebra, Mathematics - K-Theory and Homology, FOS: Mathematics, Quantum Algebra (math.QA), Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).37 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!