Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914011686109184 |
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| author | Banaian, Esther Valdivieso, Yadira |
| author_facet | Banaian, Esther Valdivieso, Yadira |
| contents | Generalized cluster algebras from orbifolds were defined by Chekhov and Shapiro to give a combinatorial description of their Teichmüller spaces. One can also assign a gentle algebra to a triangulated orbifold, as in the work of Labardini-Fragoso and Mou. In this work, we show that the Caldero-Chapoton map and the snake graph expansion map agree for arcs in triangulated orbifolds and arc modules, and similarly for closed curves and certain band modules. As a consequence, we have a bijection between some indecomposable modules over a gentle algebra and cluster variables in a generalized cluster algebra where both algebras arise from the same triangulated orbifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds Banaian, Esther Valdivieso, Yadira Representation Theory Combinatorics 13F60 05E10 05E16 Generalized cluster algebras from orbifolds were defined by Chekhov and Shapiro to give a combinatorial description of their Teichmüller spaces. One can also assign a gentle algebra to a triangulated orbifold, as in the work of Labardini-Fragoso and Mou. In this work, we show that the Caldero-Chapoton map and the snake graph expansion map agree for arcs in triangulated orbifolds and arc modules, and similarly for closed curves and certain band modules. As a consequence, we have a bijection between some indecomposable modules over a gentle algebra and cluster variables in a generalized cluster algebra where both algebras arise from the same triangulated orbifold. |
| title | Snake Graphs and Caldero-Chapoton Functions from Triangulated Orbifolds |
| topic | Representation Theory Combinatorics 13F60 05E10 05E16 |
| url | https://arxiv.org/abs/2310.16925 |