Recollements and Gorenstein projective modules for gentle algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910624042188800 |
|---|---|
| author | Liu, Yu-Zhe Liu, Dajun Ma, Xin |
| author_facet | Liu, Yu-Zhe Liu, Dajun Ma, Xin |
| contents | Let $A={\rm \mathbb{k}}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented cycle $\mathscr{C}$, which satisfies some interesting properties, for example, the tensor functor $-\otimes_A A/A\varepsilon A$ sends Gorenstein projective module $aA$ to an indecomposable projective $A/A\varepsilon A$-module; and $-\otimes_A A/A\varepsilon A$ preserves Gorenstein projective objects if any two full-relational oriented cycles do not have common vertex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08686 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recollements and Gorenstein projective modules for gentle algebras Liu, Yu-Zhe Liu, Dajun Ma, Xin Representation Theory 16G10, 16G20, 18G05 Let $A={\rm \mathbb{k}}Q/\mathcal{I}$ be a gentle algebra. We provide a bijection between non-projective indecomposable Gorenstein projective modules over $A$ and special recollements induced by an arrow $a$ on any full-relational oriented cycle $\mathscr{C}$, which satisfies some interesting properties, for example, the tensor functor $-\otimes_A A/A\varepsilon A$ sends Gorenstein projective module $aA$ to an indecomposable projective $A/A\varepsilon A$-module; and $-\otimes_A A/A\varepsilon A$ preserves Gorenstein projective objects if any two full-relational oriented cycles do not have common vertex. |
| title | Recollements and Gorenstein projective modules for gentle algebras |
| topic | Representation Theory 16G10, 16G20, 18G05 |
| url | https://arxiv.org/abs/2409.08686 |