Connections on locally trivial quantum principal fibre bundles
Dirk Calow and Rainer Matthes
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Submission date: 29. Mar. 2000
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
MSC-Numbers: 81R50, 46L87
Keywords and phrases: quantum principal bundle, differential structure, covaraint derivative, connection, q-monopole
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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.