On the Durdevic approach to quantum principal bundles
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916797159047168 |
|---|---|
| author | Del Donno, Antonio Latini, Emanuele Weber, Thomas |
| author_facet | Del Donno, Antonio Latini, Emanuele Weber, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Durdevic approach to quantum principal bundles Del Donno, Antonio Latini, Emanuele Weber, Thomas Quantum Algebra Mathematical Physics Rings and Algebras Primary 16S40, Secondary 16T05, 81R60 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. |
| title | On the Durdevic approach to quantum principal bundles |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras Primary 16S40, Secondary 16T05, 81R60 |
| url | https://arxiv.org/abs/2404.07944 |