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arXiv · 2404.07944

On the Durdevic approach to quantum principal bundles

Antonio Del Donno·Emanuele Latini·Thomas Weber
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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.

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BibTeXRIS

Antonio Del Donno, Emanuele Latini, Thomas Weber. 2024-04-11. On the Durdevic approach to quantum principal bundles. https://doi.org/10.1016/j.geomphys.2025.105567

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