# On the gauge group of Galois objects

@article{Han2020OnTG, title={On the gauge group of Galois objects}, author={Xiaoling Han and G. Landi}, journal={arXiv: Quantum Algebra}, year={2020} }

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the classical gauge groupoid of a principal bundle. When the base algebra is in the centre of the total space algebra, the gauge group of the noncommutative principal bundle is isomorphic to the group of bisections of the bialgebroid. In particular we consider Galois objects (non-trivial noncommutative bundles over a point in a sense) for which the bialgebroid is a Hopf algebra. For these… Expand

#### One Citation

Twisted Ehresmann Schauenburg bialgebroids.

- Mathematics
- 2020

We construct an invertible normalised 2 cocycle on the Ehresmann Schauenburg bialgebroid of a cleft Hopf Galois extension under the condition that the corresponding Hopf algebra is cocommutative and… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

The gauge group of a noncommutative principal bundle and twist deformations

- Mathematics, Physics
- 2018

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… Expand

Noncommutative Principal Bundles Through Twist Deformation

- Mathematics, Physics
- 2016

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the… Expand

Pullbacks and nontriviality of associated noncommutative vector bundles

- Mathematics
- 2015

Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the… Expand

Bi-Galois objects over the Taft algebras

- Mathematics
- 2000

Letk be a field. We study the groupoid of Hopf bi-Galois objects, whose objects arek-Hopf algebras, and whose morphisms areL-H-bi-Galois extensions ofk for Hopf algebrasL andH.We show that ifH=HN,m… Expand

Fibre functors of finite dimensional comodules

- Mathematics
- 1989

Let A be a commutative Hopf algebra over a field k; the k-valued fibre functors on the category of finite dimensional A-comodules correspond to Spec(A)-torsors over k as was shown by Saavedra Rivano… Expand

Principal fiber bundles in non-commutative geometry

- Mathematics
- 2016

These are the expanded notes of a course given at the Summer school “Geometric, topological, and algebraic methods for quantum field theory” held at Villa de Leyva, Colombia, in July 2015. We first… Expand

The Order of the Antipode of Finite-dimensional Hopf Algebra.

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1971

Examples of finite-dimensional Hopf algebras over a field, whose antipodes have arbitrary even orders >/=4 as mappings, are furnished. The dimension of the Hopf algebra is q(n+1), where the antipode… Expand

Translation Map in Quantum Principal Bundles

- 1994

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E(B, V,A) associated to a… Expand

General theory of lie groupoids and lie algebroids

- Mathematics
- 2005

Part I. The General Theory: 1. Lie groupoids: fundamental theory 2. Lie groupoids: algebraic constructions 3. Lie algebroids: fundamental theory 4. Lie algebroids: algebraic constructions Part II.… Expand

Monoidal Morita equivalence

- Mathematics
- 2004

The monoidal version of classical Morita theory is a theory of bialgebroids. To make this explicit we construct a bicategory the objects of which are the bialgebroids and in which equivalence of… Expand