Tilting-completion for gentle algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916713846538240 |
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| author | Chang, Wen |
| author_facet | Chang, Wen |
| contents | It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a (modified) conjecture of Happel for the case of gentle algebras. Additionally, for any $n\geq 3$ and $1\leq m \leq n-2$, there always exists a (connected) gentle algebra with rank $n$ and a pre-tilting module of rank $m$ which is not partial-tilting. The tool we use is the surface model associated with the module category of a gentle algebra. The main technique is an induction process involving surface cuts, which is hoped to be beneficial for other applications as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tilting-completion for gentle algebras Chang, Wen Representation Theory 16D90, 16E35, 57M50 It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a (modified) conjecture of Happel for the case of gentle algebras. Additionally, for any $n\geq 3$ and $1\leq m \leq n-2$, there always exists a (connected) gentle algebra with rank $n$ and a pre-tilting module of rank $m$ which is not partial-tilting. The tool we use is the surface model associated with the module category of a gentle algebra. The main technique is an induction process involving surface cuts, which is hoped to be beneficial for other applications as well. |
| title | Tilting-completion for gentle algebras |
| topic | Representation Theory 16D90, 16E35, 57M50 |
| url | https://arxiv.org/abs/2412.13971 |