Quantum principal bundles over quantum real projective spaces
Tomasz Brzezi\'nski, Bartosz Zieli\'nski

TL;DR
This paper constructs two hierarchies of quantum principal bundles over quantum real projective spaces with different structure groups, analyzing their triviality using Hopf-Galois extension criteria.
Contribution
It introduces new hierarchies of quantum principal bundles over quantum real projective spaces with U(1) and SU_q(2) as structure groups, derived via prolongation methods.
Findings
Bundles with U(1) and SU_q(2) structure groups are constructed.
The triviality of these bundles is characterized using cleft Hopf-Galois extension criteria.
Hierarchies are obtained from bundles with cyclic group of order 2 as fiber.
Abstract
Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group as a fibre. Both hierarchies are obtained by the process of prolongation from bundles with the cyclic group of order 2 as a fibre. The triviality or otherwise of these bundles is determined by using a general criterion for a prolongation of a comodule algebra to be a cleft Hopf-Galois extension.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
