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