2025/01/23 by Yunnan Li, Xiao, Yongyue, Li, Yunnan
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2501.13747
The notion of matched pair of actions on a Hopf algebra generalizes the braided group construction of Lu, Yan and Zhu, and efficiently provides Yang-Baxter operators. In this paper, we classify matched pairs of actions on the Kac-Paljutkin Hopf algebra H8. Through calculations, we obtain 6 matched pairs of actions on H8. Based on such a classification result, we find that four of them can be derived from the coquasitriangular structures of H8, while the other two can not. Furthermore, we discover that the Yang-Baxter operators associated to exactly these two distinguished matched pairs of actions are involutive.