Connections on locally trivial quantum principal fibre bundles

Dirk Calow and Rainer Matthes

Contact the author: Please use for correspondence this email.
Submission date: 29. Mar. 2000
Pages: 44
published in: Journal of geometry and physics, 1 (2002), p. 114-165 
DOI number (of the published article): 10.1016/S0393-0440(01)00050-X
Bibtex
MSC-Numbers: 81R50, 46L87
Keywords and phrases: quantum principal bundle, differential structure, covaraint derivative, connection, q-monopole
Download full preprint: PDF (567 kB), PS ziped (258 kB)

Abstract:
Budzynski and Kondracki have introduced a notion of locally trivial quantum principal fibre bundle making use of an algebraic notion of covering, which allows a reconstruction of the bundle from local pieces. Following this approach, we construct covariant differential algebras and connections on locally trivial quantum principal fibre bundles by gluing together such locally given geometric objects. We also consider covariant derivatives, connection forms, curvatures and curvature forms and explore the relations between these notions. As an example, a U(1) quantum principal bundle over a glued quantum sphere as well as a connection in this bundle is constructed. The connection may be considered as a q-deformed Dirac monopole.