Place:

This talk will take place in the blue seminar room, back building, Žitná 25.

It will also be broadcast on Zoom:

https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09

Meeting ID: 919 7518 3920

Passcode: 102707

Abstract:

In noncommutative geometry Hopf–Galois extensions generalize the concept of principal bundle. Given a covariant first order differential calculus on the total space algebra there are natural notions of base forms and horizontal forms. If the covariant calculus on the structure Hopf algebra is compatible with the former, in the sense that the vertical map constitutes a short exact sequence, we have a principal differential calculus. Then, the faithfully flat Hopf–Galois extension amplifies to a Hopf–Galois extensions of graded objects. In this talk we give a sheaf-theoretic approach to principal differential calculi. This is required in the presence of projective bases, where global sections are trivial and the local information is crucial. The theory is elucidated by the explicit example of q-deformed SL(2,\mathbb{C}) endowed with its covariant calculi.