Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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| author | Fang, Xin Gorsky, Mikhail Palu, Yann Plamondon, Pierre-Guy Pressland, Matthew |
| author_facet | Fang, Xin Gorsky, Mikhail Palu, Yann Plamondon, Pierre-Guy Pressland, Matthew |
| contents | We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpretation of such quotients: they appear as prototypical examples of a new construction of quotients of extriangulated categories by ideals generated by morphisms from injectives to projectives. We apply our results to Frobenius exact cluster categories and Higgs categories with suitable relative extriangulated structures, and to categories of walks related to gentle algebras. In all three cases, the extriangulated structures are well-behaved (they are 0-Auslander) and their quotients are equivalent to homotopy categories of two-term complexes of projectives over suitable finite-dimensional algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05524 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extriangulated ideal quotients, with applications to cluster theory and gentle algebras Fang, Xin Gorsky, Mikhail Palu, Yann Plamondon, Pierre-Guy Pressland, Matthew Representation Theory We extend results of Brüstle-Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpretation of such quotients: they appear as prototypical examples of a new construction of quotients of extriangulated categories by ideals generated by morphisms from injectives to projectives. We apply our results to Frobenius exact cluster categories and Higgs categories with suitable relative extriangulated structures, and to categories of walks related to gentle algebras. In all three cases, the extriangulated structures are well-behaved (they are 0-Auslander) and their quotients are equivalent to homotopy categories of two-term complexes of projectives over suitable finite-dimensional algebras. |
| title | Extriangulated ideal quotients, with applications to cluster theory and gentle algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2308.05524 |