• Corpus ID: 245704352

Hopf algebroids from noncommutative bundles

@inproceedings{Han2022HopfAF,
  title={Hopf algebroids from noncommutative bundles},
  author={Xiao-Wei Han and Giovanni Landi and Yang Liu},
  year={2022}
}
We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to deforming a quantum homogeneous space; this needs a careful deformation of the structure Hopf algebra in order to preserve the compatibilities between the Hopf algebra operations. 

References

SHOWING 1-10 OF 20 REFERENCES

Principal Fibrations from Noncommutative Spheres

We construct noncommutative principal fibrations Sθ7→Sθ4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to

Noncommutative Principal Bundles Through Twist Deformation

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

Gauge groups and bialgebroids

We study the Ehresmann–Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the gauge groupoid of a classical principal bundle. We show that the gauge group of the

Quantum Symmetry Groups of Noncommutative Spheres

Abstract: We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which

Representation theory of Hopf galois extensions

LetH be a Hopf algebra over the fieldk andB ⊂A a right faithfully flat rightH-Galois extension. The aim of this paper is to study some questions of representation theory connected with the ring

Principal homogeneous spaces for arbitrary Hopf algebras

LetH be a Hopf algebra over a field with bijective antipode,A a rightH-comodule algebra,B the subalgebra ofH-coinvariant elements and can:A ⊗BA →A ⊗H the canonical map. ThenA is a faithfully flat (as

Noncommutative Manifolds, the Instanton Algebra¶and Isospectral Deformations

Abstract: We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn. They arise naturally from basic considerations of noncommutative

Noncommutative Finite-Dimensional Manifolds. I. Spherical Manifolds and Related Examples

Abstract: We exhibit large classes of examples of noncommutative finite-dimensional manifolds which are (non-formal) deformations of classical manifolds. The main result of this paper is a complete

Bialgebras Over Noncommutative Rings and a Structure Theorem for Hopf Bimodules

TLDR
A class of algebras whose module categories are also monoidal categories; however, the underlying functor to the category of k-vector spaces fails to be monoidal, it is shown that there is a suitable underlyingFunctor toThe category of B-bimodules over a k-algebra B which is monoidal with respect to the tensor product over B.