Infinitesimal H-pseudobialgebra and associative pseudo-Yang-Baxter equation

Abstract

This article aims to study infinitesimal H-pseudobialgebra and associative pseudo-Yang-Baxter equation. Firstly, we define infinitesimal H-pseudobialgebra, which is an associative analog of Lie H-pseudobialgebra. We also obtain the associative pseudo-Yang-Baxter equation over an associative H-pseudoalgebra. Next, we establish the connections between infinitesimal H-pseudobialgebra and Lie H-pseudobialgebra, associative pseudo-Yang-Baxter equation and classical pseudo-Yang-Baxter equation. Finally, the annihilation algebra of an associative H-pseudoalgebra is discussed.

Keywords:

• Associative H-pseudoalgebra
• infinitesimal bialgebra
• Lie H-pseudobialgebra
• Yang-Baxter equation

2020 Mathematics Subject Classification:

• 16T05
• 16T25
• 17B62

Acknowledgments

The authors are deeply indebted to the referee for his/her very useful suggestions and some improvements to the original manuscript.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 12101188, 11871144) and Doctoral Fund of Henan Institute of Technology (No. KQ2003).