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Nontrivial Deformation of a Trivial Bundle
Piotr M. Hajacab, Bartosz Zielińskic a Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, 00-956 Warszawa, Poland
b Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski,
ul. Hoża 74, 00-682 Warszawa, Poland
c Department of Computer Science, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153 90-236 Łódź, Poland
Abstract:
The ${\rm SU}(2)$-prolongation of the Hopf fibration $S^3\to S^2$ is a trivializable principal ${\rm SU}(2)$-bundle. We present a noncommutative deformation of this bundle to a quantum principal ${\rm SU}_q(2)$-bundle that is not trivializable. On the other hand, we show that the ${\rm SU}_q(2)$-bundle is piecewise trivializable with respect to the closed covering of $S^2$ by two hemispheres intersecting at the equator.
Keywords:
quantum prolongations of principal bundles; piecewise trivializable quantum principal bundles.
Received: October 29, 2013; in final form March 3, 2014; Published online March 27, 2014
Citation:
Piotr M. Hajac, Bartosz Zieliński, “Nontrivial Deformation of a Trivial Bundle”, SIGMA, 10 (2014), 031, 7 pp.
Linking options:
https://www.mathnet.ru/eng/sigma896 https://www.mathnet.ru/eng/sigma/v10/p31
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Abstract page: | 356 | Full-text PDF : | 29 | References: | 37 |
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