Multiplicative properties of certain elements in Bridgeland Hall algebras

Abstract

Let A be a finite dimensional algebra of finite global dimension over a finite field. In the present paper, we introduce certain elements in the Bridgeland Hall algebra of A, and give a multiplication formula for these elements. In particular, this generalizes the main result in Geng and Peng (2015, J. Algebra 437:116–132).

Keywords:

• Bridgeland Hall algebra
• multiplicative property
• Ringel–Hall algebra

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16G20
• 17B20
• 17B37

Acknowledgments

The authors would like to thank the anonymous referee for his/her efficient review, and they are also grateful to Bangming Deng for stimulating discussions and valuable comments.

Additional information

Funding

The first author is supported by the National Natural Science Foundation of China (no. 11701090) and Natural Science Foundation of Fujian Province of China (no. 2017J05004). The second author is supported by the National Natural Science Foundation of China (no. 11801273), Natural Science Foundation of Jiangsu Province of China (no. BK20180722) and Natural Science Foundation of Jiangsu Higher Education Institutions of China (no. 18KJB110017).