The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911225545228288 |
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| author | Chen, Hui Yang, Dong |
| author_facet | Chen, Hui Yang, Dong |
| contents | Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$. As a consequence, it is shown that the triangle structure of such derived categories is uniquely determined by the underlying additive category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure Chen, Hui Yang, Dong Representation Theory 16E35, 16E45, 18G80 Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$. As a consequence, it is shown that the triangle structure of such derived categories is uniquely determined by the underlying additive category. |
| title | The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure |
| topic | Representation Theory 16E35, 16E45, 18G80 |
| url | https://arxiv.org/abs/2510.15252 |