Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913111607345152 |
|---|---|
| author | Kowalzig, Niels Weber, Thomas |
| author_facet | Kowalzig, Niels Weber, Thomas |
| contents | We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider equivalence in the realm of Hopf algebroids. The resulting categorical equivalences enable us to classify covariant calculi on Hopf algebroids and, more in general, covariant calculi on quantum homogeneous spaces in this context, in terms of substructures of the augmentation ideal. This generalises the well-known classification results of Woronowicz and Hermisson. A particular focus is given on examples, including covariant calculi on the Ehresmann-Schauenburg Hopf algebroid of a faithfully flat Hopf-Galois extension, and covariant calculi on scalar extension Hopf algebroids, as well as homogeneous space variants of the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids Kowalzig, Niels Weber, Thomas Quantum Algebra Category Theory We develop a notion of covariant differential calculus for Hopf algebroids. As a byproduct, we prove analogues of the fundamental theorem of Hopf modules and a Takeuchi-Schneider equivalence in the realm of Hopf algebroids. The resulting categorical equivalences enable us to classify covariant calculi on Hopf algebroids and, more in general, covariant calculi on quantum homogeneous spaces in this context, in terms of substructures of the augmentation ideal. This generalises the well-known classification results of Woronowicz and Hermisson. A particular focus is given on examples, including covariant calculi on the Ehresmann-Schauenburg Hopf algebroid of a faithfully flat Hopf-Galois extension, and covariant calculi on scalar extension Hopf algebroids, as well as homogeneous space variants of the latter. |
| title | Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids |
| topic | Quantum Algebra Category Theory |
| url | https://arxiv.org/abs/2507.16455 |