Name: On the Đurđević approach to quantum principal bundles
Keywords: Rings and Algebras, Noncommutative geometry (à la Connes), Quantum principal bundle; Hopf-Galois extension; Noncommutative differential calculus; Strong connection; Braided-commutative algebra, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), FOS: Physical sciences, Mathematical Physics (math-ph), strong connections, Quantum Algebra, quantum principal bundles, Hopf algebras, quantum groups and related topics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 216, page 105,567 (issn: 0393-0440,

Authors: Del Donno A.; Latini E.; Weber T.;

doi: 10.1016/j.geomphys.2025.105567 , 10.2139/ssrn.4880683 , 10.48550/arxiv.2404.07944

arXiv: 2404.07944

handle: 11585/1026384

On the Đurđević approach to quantum principal bundles

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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.

45 pages; corrected equation (206); added "Quantum Symmetries" to acknowledgements; added journal reference for [11]

Related Organizations

National Institute for Nuclear Physics
Italy
Alma Mater Studiorum University of Bologna
Italy
INFN Sezione di Bologna
Italy

Keywords

Rings and Algebras, Noncommutative geometry (à la Connes), Quantum principal bundle; Hopf-Galois extension; Noncommutative differential calculus; Strong connection; Braided-commutative algebra, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), FOS: Physical sciences, Mathematical Physics (math-ph), strong connections, Quantum Algebra, quantum principal bundles, Hopf algebras, quantum groups and related topics, Rings and Algebras (math.RA), braided-commutative algebras, FOS: Mathematics, Hopf-Galois extensions, Quantum Algebra (math.QA), Primary 16S40, Secondary 16T05, 81R60, noncommutative differential calculus, Mathematical Physics

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