A geometric model for semilinear locally gentle algebras
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917584506454016 |
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| author | Banaian, Esther Bennett-Tennenhaus, Raphael Jacobsen, Karin M. Wright, Kayla |
| author_facet | Banaian, Esther Bennett-Tennenhaus, Raphael Jacobsen, Karin M. Wright, Kayla |
| contents | We consider certain generalizations of gentle algebras that we call semilinear locally gentle algebras. These rings are examples of semilinear clannish algebras as introduced by the second author and Crawley-Boevey. We generalise the notion of a nodal algebra from work of Burban and Drozd and prove that semilinear gentle algebras are nodal by adapting a theorem of Zembyk. We also provide a geometric realization of Zembyk's proof, which involves cutting the surface into simpler pieces in order to endow our locally gentle algebra with a semilinear structure. We then consider this surface glued back together, with the seams in place, and use it to give a geometric model for the finite-dimensional modules over the semilinear locally gentle algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric model for semilinear locally gentle algebras Banaian, Esther Bennett-Tennenhaus, Raphael Jacobsen, Karin M. Wright, Kayla Representation Theory Primary 16G20, Secondary 05E10, 05C10, 16D90 We consider certain generalizations of gentle algebras that we call semilinear locally gentle algebras. These rings are examples of semilinear clannish algebras as introduced by the second author and Crawley-Boevey. We generalise the notion of a nodal algebra from work of Burban and Drozd and prove that semilinear gentle algebras are nodal by adapting a theorem of Zembyk. We also provide a geometric realization of Zembyk's proof, which involves cutting the surface into simpler pieces in order to endow our locally gentle algebra with a semilinear structure. We then consider this surface glued back together, with the seams in place, and use it to give a geometric model for the finite-dimensional modules over the semilinear locally gentle algebra. |
| title | A geometric model for semilinear locally gentle algebras |
| topic | Representation Theory Primary 16G20, Secondary 05E10, 05C10, 16D90 |
| url | https://arxiv.org/abs/2402.04947 |