Quantum Principal Fiber Bundles: Topological Aspects

Details Quantum Principal Fiber Bundles: Topological Aspects Quantum Principal Fiber Bundles: Topological Aspects

1994-01-06

arxiv.org/abs/hep-th/9401019v1

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, LaTeX, IM PAN preprint # 517

Scientific paper

We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum bundle admits sections if and only if it is trivial. Using a quantum version of \v{C}ech cocycles, we obtain a reconstruction theorem for quantum principal bundles. The classification of bundles over a given quantum space as a base space is reduced to the corresponding problem, but with an ordinary classical group playing the role of structure group. Some explicit examples are considered.

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