Hopf fibration and monopole connection over the contact quantum spheres
arXiv:math/0301123 · doi:10.1016/j.geomphys.2003.09.009
Abstract
Noncommutative geometry of quantised contact spheres introduced by Omori, Maeda, Miyazaki and Yoshioka is studied. In particular it is proven that these spheres form a noncommutative Hopf fibration in the sense of Hopf-Galois extensions. The monopole (strong) connection is constructed, and projectors describing projective modules of all monopole charges are computed.
arXiv comment15 pages, LaTeX
References in corpus (13)
- Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
- Quantum group gauge theory on quantum spaces
- Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples
- Coalgebra Gauge Theory
- Strong Connections on Quantum Principal Bundles
- Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory
- Projective module description of the q-monopole
- Noncommutative Instantons on the 4-Sphere from Quantum Groups
- Instantons on the Quantum 4-Spheres S^4_q
- Connections on locally trivial quantum principal fibre bundles
- Bijectivity of the canonical map for the noncommutative instanton bundle
- Quantum geometry of algebra factorisations and coalgebra bundles
- Dirac monopoles from the Matsumoto non-commutative spheres