Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.00729 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913338958544896 |
|---|---|
| author | Cruz, Tiago |
| author_facet | Cruz, Tiago |
| contents | The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided.
In particular, given two split quasi-hereditary algebras $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over $A$ and the smallest resolving subcategory containing all standard modules over $B$ lifts to a Morita equivalence between $A$ and $B$ which preserves the quasi-hereditary structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic tilting modules and Ringel duality in the Noetherian world Cruz, Tiago Representation Theory Rings and Algebras 16G30 (Primary) 16D10 (Secondary) The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over $A$ and the smallest resolving subcategory containing all standard modules over $B$ lifts to a Morita equivalence between $A$ and $B$ which preserves the quasi-hereditary structure. |
| title | Characteristic tilting modules and Ringel duality in the Noetherian world |
| topic | Representation Theory Rings and Algebras 16G30 (Primary) 16D10 (Secondary) |
| url | https://arxiv.org/abs/2405.00729 |