On the Durdevic approach to quantum principal bundles

Autor:	Del Donno, Antonio, Latini, Emanuele, Weber, Thomas
Rok vydání:	2024
Předmět:	Mathematics - Quantum Algebra Mathematical Physics Mathematics - Rings and Algebras Primary 16S40 Secondary 16T05 81R60
Druh dokumentu:	Working Paper
Popis:	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. Comment: 45 pages; corrected equation (206); added "Quantum Symmetries" to acknowledgements; added journal reference for [11]
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.07944 Zobrazit plný text záznamu View this record from Arxiv