Thomas Weber (University of Turin):
Hopf-Galois extension in noncommutative differential geometry
Time and place
Monday, 13.3.23, 15:00-16:00, Raum 404, Ernst-Zermelo-Str. 1
Abstract
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.