Piotr M. Hajac: Braided noncommutative join construction

We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show that this coaction is principal. Our examples are built from the noncommutative torus with the natural free action of the classical torus, and arbitrary anti-Drinfeld doubles of finite-dimensional Hopf algebras. The former yields a noncommutative deformation of a non-trivial torus bundle, and the latter a finite quantum covering. (Based on joint work with L. Dabrowski, T. Hadfield and E. Wagner.)

The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. (18.09.2014)