Chiara Pagani

In noncommutative geometry, Hopf-Galois extensions are seen as principal bundles.

We study gauge transformations of K-equivariant H-Galois extensions, for K a triangular Hopf algebra. Each such noncommutative principal bundle can be associated a sequence of braided Lie algebras (Lie algebras in the symmetric monoidal category of K-modules), a noncommutative analogue of the Atiyah sequence of a principal bundle. Connections are then given by splittings of the sequence.

Examples for bundles over noncommutative spheres are presented.

Based on joint works with Paolo Aschieri and Giovanni Landi.