Locally noetherian quiver representations
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909284331159552 |
|---|---|
| author | Krause, Henning |
| author_facet | Krause, Henning |
| contents | It is shown that a quiver is left noetherian if and only if the category of quiver representations in any locally noetherian abelian category is again locally noetherian. Here, locally noetherian means that any object is the directed union of its noetherian subobjects. For a quiver to be left noetherian means that the left ideals of paths starting at any fixed vertex satisfy the ascending chain condition. The proof generalises to representations of any small category that admits a Gröbner enrichment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally noetherian quiver representations Krause, Henning Representation Theory Category Theory Rings and Algebras 16G20 (primary), 18E10 (secondary) It is shown that a quiver is left noetherian if and only if the category of quiver representations in any locally noetherian abelian category is again locally noetherian. Here, locally noetherian means that any object is the directed union of its noetherian subobjects. For a quiver to be left noetherian means that the left ideals of paths starting at any fixed vertex satisfy the ascending chain condition. The proof generalises to representations of any small category that admits a Gröbner enrichment. |
| title | Locally noetherian quiver representations |
| topic | Representation Theory Category Theory Rings and Algebras 16G20 (primary), 18E10 (secondary) |
| url | https://arxiv.org/abs/2408.05405 |