Stability Conditions and Harder-Narasimhan Filtrations for Triangulated Categories (2512.21546v1)

Published 25 Dec 2025 in math.RT

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 $ε_γ$. 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 $D^{b(\mathrm{rep}} A_2)$.

Abstract PDF Chat (Pro)

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper to Video (Beta)

Generate a video overview of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

Collections

Sign up for free to add this paper to one or more collections.

Tweets

Sign up for free to view the 2 tweets with 4 likes about this paper.

Sign Up for Free