Mutation of $n$-cotorsion pairs in triangulated categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910426627833856 |
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| author | Chang, Huimin Zhou, Panyue |
| author_facet | Chang, Huimin Zhou, Panyue |
| contents | In this article, we define the notion of $n$-cotorsion pairs in triangulated categories, which is a generalization of the classical cotorsion pairs. We prove that any mutation of an $n$-cotorsion pair is again an $n$-cotorsion pair. When $n=1$, this result generalizes the work of Zhou and Zhu for classical cotorsion pairs. As applications, we give a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A$ and give a geometric realization of mutation of $n$-cotorsion pairs via rotation of certain configurations of $n$-diagonals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutation of $n$-cotorsion pairs in triangulated categories Chang, Huimin Zhou, Panyue Representation Theory Category Theory In this article, we define the notion of $n$-cotorsion pairs in triangulated categories, which is a generalization of the classical cotorsion pairs. We prove that any mutation of an $n$-cotorsion pair is again an $n$-cotorsion pair. When $n=1$, this result generalizes the work of Zhou and Zhu for classical cotorsion pairs. As applications, we give a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A$ and give a geometric realization of mutation of $n$-cotorsion pairs via rotation of certain configurations of $n$-diagonals. |
| title | Mutation of $n$-cotorsion pairs in triangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2404.18336 |