Matched pairs, post-Hopf algebras and the quantum Yang-Baxter equation

22.11.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Yunan Li (Guangzhong, China) (online)

Recently, Ferri and Sciandra introduced two equivalent notions, matched pair of actions on a Hopf algebra and Yetter-Drinfeld brace. Any of these objects actually provides a solution of the quantum Yang-Baxter equation, generalizing the construction of Yang-Baxter operators by Lu, Yan and Zhu from braiding operator on a group, and also by Angiono, Galindo and Vendramin from a cocommutative Hopf brace.
     Later, Sciandra ingeniously proposed one more equivalent notion, namely Yetter-Drinfeld post-Hopf algebra, as a non-cocommutative generalization of post-Hopf algebra formerly introduced by Sheng, Tang and me, and most remarkably it provides a sub-adjacent structure as cocommutative post-Hopf algebra does.
     In this talk, I intend to review these works first, and then discuss some related problems.

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