We study noncommutative principal bundles (Hopf–Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space subalgebra is central, we define the gauge group as the group of vertical automorphisms or equivalently as the group of equivariant algebra maps. We study Drinfeld twist (2-cocycle) deformations of Hopf–Galois extensions and show that the gauge group of the twisted extension is isomorphic to the gauge group of the initial extension. In particular, non- commutative principal bundles arising via twist deformation of commutative principal bundles have classical gauge group. We illustrate the theory with a few examples.
The gauge group of a noncommutative principal bundle and twist deformations
Landi, Giovanni
;Pagani, Chiara
2020-01-01
Abstract
We study noncommutative principal bundles (Hopf–Galois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasi-commutative, and thus the base space subalgebra is central, we define the gauge group as the group of vertical automorphisms or equivalently as the group of equivariant algebra maps. We study Drinfeld twist (2-cocycle) deformations of Hopf–Galois extensions and show that the gauge group of the twisted extension is isomorphic to the gauge group of the initial extension. In particular, non- commutative principal bundles arising via twist deformation of commutative principal bundles have classical gauge group. We illustrate the theory with a few examples.File | Dimensione | Formato | |
---|---|---|---|
JNCG-2020-014-004-06.pdf
Accesso chiuso
Tipologia:
Documento in Versione Editoriale
Licenza:
Copyright Editore
Dimensione
571.58 kB
Formato
Adobe PDF
|
571.58 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.