Extensions in Jacobian algebras via punctured skein relations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866917096217116672 |
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| author | Dominguez, Salomon Elsener, Ana Garcia |
| author_facet | Dominguez, Salomon Elsener, Ana Garcia |
| contents | Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type $D$ and in a punctured surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_07844 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extensions in Jacobian algebras via punctured skein relations Dominguez, Salomon Elsener, Ana Garcia Representation Theory Rings and Algebras 16G20, 16E30, 13F60 Given a Jacobian algebra arising from the punctured disk, we show that all non-split extensions can be found using the tagged arcs and skein relations previously developed in cluster algebras theory. Our geometric interpretation can be used to find non-split extensions over other Jacobian algebras arising form surfaces with punctures. We show examples in type $D$ and in a punctured surface. |
| title | Extensions in Jacobian algebras via punctured skein relations |
| topic | Representation Theory Rings and Algebras 16G20, 16E30, 13F60 |
| url | https://arxiv.org/abs/2108.07844 |