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Hopf-Galois extension in noncommutative differential geometry

Thomas Weber (University of Turin)

Montag, 13. März 2023 15:00Uhr

In this seminar I give a gentle introduction to the theory of Hopf-Galois extensions and their role in noncommutative differential geometry. From a geometric point of view they correspond to principal bundles on noncommutative algebras with a Hopf algebra replacing the structure group. Principality of such a bundle can equivalently be phrased in terms of a noncommutative Atiyah sequence. We continue by discussing differential calculi on Hopf-Galois extensions, proving that in the faithfully flat case such a calculus amplifies to a graded Hopf-Galois extensions if and only if the corresponding Atiyah sequence is exact, as well. As an example we discuss the q-monopole fibration. The presentation is partially based on a collaboration with Aschieri, Fioresi and Latini.