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Title: Methods of constructing quantum principal bundles
Author: Zielinzki, B. P.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2005
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In this thesis two new methods of constructing non-commutative principal bundles or coalgebra Galois extensions are presented. The first method is based on the use of the cotensor product of coalgebra Galois extensions and can be seen as a generalization of the prolongation theory. Sufficient conditions for the cotensor product of quantum principal bundles (with strong connections) to give a new quantum principal bundle (with a strong connections) to give a new quantum principal bundle (with a strong connection) are derived. The second method uses the covering and gluing procedures developed by Calow and Matthes. The notion of a locally coalgebra Galois extension is introduced and conditions are derived for such an extension to be a (globally) coalgebra Galois extension. These constructions are illustrated by explicit examples based on non-commutative Hopf fibration. Also a new non-commutative Hopf fibration is presented, derived from the quantisation of a contact structure on the three-sphere.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available