TY - JOUR
T1 - Deformation quantization of principal bundles
AU - Aschieri, Paolo
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - 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 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.
AB - 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 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.
KW - Hopf-Galois extensions
KW - Noncommutative geometry
KW - cocycle twisting
KW - noncommutative principal bundles
UR - http://www.scopus.com/inward/record.url?scp=84981523385&partnerID=8YFLogxK
U2 - 10.1142/S0219887816300105
DO - 10.1142/S0219887816300105
M3 - Article
SN - 0219-8878
VL - 13
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
IS - 8
M1 - 1630010
ER -