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MiS Preprint
22/2000

Connections on locally trivial quantum principal fibre bundles

Dirk Calow and Rainer Matthes

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.

Received:
Mar 29, 2000
Published:
Mar 29, 2000
MSC Codes:
81R50, 46L87
Keywords:
quantum principal bundle, differential structure, covaraint derivative, connection, q-monopole

Related publications

inJournal
2002 Repository Open Access
Dirk Calow and Rainer Matthes

Connections on locally trivial quantum principal fibre bundles

In: Journal of geometry and physics, 1 (2002), pp. 114-165