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arXiv · 2512.21546

Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories

Wenyu Gao·Fan Xu
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Abstract

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 $\epsilon_\gamma$. 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 $D^b(\mathrm{rep} A_2)$.

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BibTeXRIS

Wenyu Gao, Fan Xu. 2025-12-25. Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories. https://arxiv.org/abs/2512.21546

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