abstract LjubljanaGeom2014

Seminar in geometry, Ljubljana, May 5, 2014 (10:15-11:45 am)

Zoran Škoda: Čech cocycles for noncommutative principal bundles

Hopf algebras often play role of the symmetries in noncommutative geometry. However, there is no notion of an open set, so it is hard to make sense of local trivializations. One of the possible replacements for open sets are the localization functors. For principal bundles one of the possible frameworks is the framework of Hopf-Galois extensions. Using localizations we introduce a finer class of the locally trivial Hopf-Galois extensions, and, more importantly, the global objects which generalize Hopf-Galois picture and which in some cover by coaction compatible localizations reduce to it. Classification of bundles then reduces to a Cech like cocycles with coefficients in a Hopf algebra. The examples of bundles on quantum flag varieties which I considered earlier without Cech picture fit into this context (with applications like quantum group coherent states).

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