Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908731823882240 |
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| author | Gao, Wenyu Xu, Fan |
| author_facet | Gao, Wenyu Xu, Fan |
| contents | In this paper, we investigate the relationships between Harder-Narasimhan filtrations and derived Hall algebras. We extend several results from abelian categories to triangulated categories, including Reineke inversions, wall-crossing formulas, and Joyce's elements $ε_γ$. The results in triangulated categories can be summarized via a diagram of the same form of that in abelian categories. As an application, we characterize all possibilities for stability conditions on $D^b(\mathrm{rep} A_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories Gao, Wenyu Xu, Fan Representation Theory In this paper, we investigate the relationships between Harder-Narasimhan filtrations and derived Hall algebras. We extend several results from abelian categories to triangulated categories, including Reineke inversions, wall-crossing formulas, and Joyce's elements $ε_γ$. The results in triangulated categories can be summarized via a diagram of the same form of that in abelian categories. As an application, we characterize all possibilities for stability conditions on $D^b(\mathrm{rep} A_2)$. |
| title | Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.21546 |