Deformation quantization of principal bundles
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 HopfGalois 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 automorphisms 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.
 Publication:

International Journal of Geometric Methods in Modern Physics
 Pub Date:
 August 2016
 DOI:
 10.1142/S0219887816300105
 arXiv:
 arXiv:1611.01493
 Bibcode:
 2016IJGMM..1330010A
 Keywords:

 Noncommutative geometry;
 noncommutative principal bundles;
 Hopf–Galois extensions;
 cocycle twisting;
 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 20 pages. Contribution to the volume in memory of Professor Mauro Francaviglia. Based on joint work with Pierre Bieliavsky, Chiara Pagani and Alexander Schenkel