Alessandro Carotenuto

We introduce a simple but effective framework to build examples of principal comodule algebras, the quantum analogue of principal fibrations. Here the total space and the basis of the fbration are quantum homogeneous spaces of a given Hopf algebra A, while the role of the structure group is played by a certain Hopf subalgebra of A. We also show how one can relax these assumptions in order to get a generalization of the usual notion of an Hopf--Galois extension that falls into the framework recently proposed by Brzezinski and Szymanski as Noncommutative analogues of fibrations with homogeneous fibre. In both cases, we will present a number of concrete examples with quantum flag manifolds.