Artin-Schelter Gorenstein property of Hopf Galois extensions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915670091890688 |
|---|---|
| author | Zhu, Ruipeng |
| author_facet | Zhu, Ruipeng |
| contents | This paper investigates the homological properties of the faithfully flat Hopf Galois extension $A \subseteq B$. It establishes that when $B$ is a noetherian affine PI algebra and $A$ is AS Gorenstein, $B$ inherits the AS Gorenstein property. Furthermore, we demonstrate that injective dimension serves as a monoidal invariant for AS Gorenstein Hopf algebras. Specifically, if two such Hopf algebras have equivalent monoidal categories of comodules, then their injective dimensions are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Artin-Schelter Gorenstein property of Hopf Galois extensions Zhu, Ruipeng Rings and Algebras 16E65, 16E10, 16T05 This paper investigates the homological properties of the faithfully flat Hopf Galois extension $A \subseteq B$. It establishes that when $B$ is a noetherian affine PI algebra and $A$ is AS Gorenstein, $B$ inherits the AS Gorenstein property. Furthermore, we demonstrate that injective dimension serves as a monoidal invariant for AS Gorenstein Hopf algebras. Specifically, if two such Hopf algebras have equivalent monoidal categories of comodules, then their injective dimensions are equal. |
| title | Artin-Schelter Gorenstein property of Hopf Galois extensions |
| topic | Rings and Algebras 16E65, 16E10, 16T05 |
| url | https://arxiv.org/abs/2501.02828 |