Connections on locally trivial quantum principal fibre bundles
arXiv:math/0002228 · doi:10.1016/S0393-0440(01)00050-X
Abstract
Following the approach of Budzyński and Kondracki, we define covariant differential algebras and connections on locally trivial quantum principal fibre bundles. We also consider covariant derivatives, connection forms and curvatures and explore the relations between these notions. As an example, a U(1) quantum principal bundle over a glued quantum sphere and a connection in this bundle is constructed. This connection may be interpreted as a q-deformed Dirac monopole.
42 pages
References in corpus (14)
- The quantum structure of spacetime at the Planck scale and quantum fields
- Quantum group gauge theory on quantum spaces
- Geometry of Quantum Principal Bundles I
- Strong Connections on Quantum Principal Bundles
- Translation map in quantum principal bundles
- Supersymmetric quantum theory and (non-commutative) differential geometry
- Quantum Groups on Fibre Bundles
- Covering and gluing of algebras and differential algebras
- General compact quantum groups, a tutorial
- On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes
- String/Quantum Gravity motivated Uncertainty Relations and Regularisation in Field Theory
- Quantum Principal Fiber Bundles: Topological Aspects
- Locally trivial quantum vector bundles and associated vector bundles
- Gauge transformations on locally trivial quantum principal fibre bundles
Cited by in corpus (9)
- Hopf fibration and monopole connection over the contact quantum spheres
- Locally coalgebra-Galois extensions
- Weighted circle actions on the Heegaard quantum sphere
- Reductions of piecewise-trivial principal comodule algebras
- Classical Principal Fibre Bundles from a Quantum Group Viewpoint
- Piecewise Principal Coactions of Co-Commutative Hopf Algebras
- A locally trivial quantum Hopf bundle
- Toeplitz algebras in quantum Hopf fibrations
- 50 Years of Gauge Theory. Mathematical Aspects