Hopf algebroids from noncommutative bundles

TL;DR

This paper introduces two classes of Hopf algebroids derived from noncommutative principal bundles, involving deformations of structures and quantum spaces to maintain algebraic compatibilities.

Contribution

It provides new constructions of Hopf algebroids from noncommutative bundles, expanding understanding of their algebraic deformations and compatibilities.

Findings

Two classes of Hopf algebroids constructed from noncommutative principal bundles

Deformation techniques preserve algebraic structures in quantum spaces

Enhanced understanding of noncommutative geometric structures

Abstract

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.