Stability conditions and derived Hall algebras

Abstract

In the present paper, we investigate the universal PBW basis and HN system for the derived Hall algebra of a triangulated category satisfying some finiteness conditions. Furthermore, we study the related stability conditions on the module category $\mathcal{A}$ of the path algebra A of an acyclic quiver and on the bounded derived category of $\mathcal{A}$. Moreover, we investigate the relation between the Ringel-Hall algebra and the HN system of A defined by Reineke.

Keywords:

• Derived Hall algebra
• HN system
• stability condition

2020 Mathematics Subject Classification:

• 16G20
• 16G70

Acknowledgments

The authors would like to express their great gratitude to the referee for carefully reading the manuscript and many suggestions, which helped to improve the readability and quality of the paper. The authors are also very grateful to Professor Bangming Deng for his careful guidance and discussions.

Additional information

Funding

The first author was supported by the Fundamental Research Funds for the Central Universities (No. 2022YQLX02) and the National Natural Science Foundation of China (Grant Nos. 11901567, 12061060, 12271321).