Deformation quantization of principal bundles
arXiv:1611.01493 · doi:10.1142/S0219887816300105
Abstract
We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles, and more in general to the deformation of Hopf-Galois extensions. First we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next we twist deform a subgroup of the group of authomorphisms of the principal bundle, and this leads to a noncommutative base space. Considering both deformations we obtain noncommutative principal bundles with noncommutative fiber and base space as well.
arXiv comment20 pages. Contribution to the volume in memory of Professor Mauro Francaviglia. Based on joint work with Pierre Bieliavsky, Chiara Pagani and Alexander Schenkel
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