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We present two classes of examples of Hopf algebroids associated with non-commutative 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.

AMSC: 81R50, 55R10, 18G45


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