On the Durdevic approach to quantum principal bundles
Quantum Algebra
2025-06-19 v3 Mathematical Physics
math.MP
Rings and Algebras
Abstract
We revisit and extend the Durdevic theory of complete calculi on quantum principal bundles. In this setting one naturally obtains a graded Hopf-Galois extension of the higher order calculus and an intrinsic decomposition of degree 1-forms into horizontal and vertical forms. This proposal is appealing, since it is consistently equipped with a canonical braiding and exactness of the Atiyah sequence is guaranteed. Moreover, we provide examples of complete calculi, including the noncommutative 2-torus, the quantum Hopf fibration and differential calculi on crossed product algebras.
Cite
@article{arxiv.2404.07944,
title = {On the Durdevic approach to quantum principal bundles},
author = {Antonio Del Donno and Emanuele Latini and Thomas Weber},
journal= {arXiv preprint arXiv:2404.07944},
year = {2025}
}
Comments
45 pages; corrected equation (206); added "Quantum Symmetries" to acknowledgements; added journal reference for [11]