走向现代数学学术报告 - 徐楠燕博士生（No. 793)
报告题目：Algebraic structures related to the Yang-Baxter equation
报告摘要：We clarified the relations between various constructions of solutions of the Yang-Baxter equation (YBE) from Leibniz algebras, racks, 3-Leibniz algebras,3-racks, linear racks, trilinear racks, and give new constructions of solutions of the Yang-Baxter equation.
Next, we consider the Zamolochikov Tetrahedron equation (ZTE), which is the generalization of the YBE. We introduce notions of central Leibniz 2-algebras and linear 2-racks, where central Leibniz algebras and linear racks serve as their decategorifications. We show that central Leibniz 2-algebras and linear 2-racks give rise to solutions of the ZTE, and the decategorization of these results exactly corresponds to the cases in the YBE.
