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 of the path algebra A of an acyclic quiver and on the bounded derived category of
. Moreover, we investigate the relation between the Ringel-Hall algebra and the HN system of A defined by Reineke.
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.