椭圆曲线退化的向量丛与杨-巴克斯特方程

经典杨-巴克斯特方程与$A_{\infty}$ -约束

Classical Yang-Baxter equation and the $A_{\infty}$-constraint

证明了经典的杨-巴克斯特方程的椭圆解可以由椭圆曲线上的三重Massey乘积得到.我们引入了这个方程的结合形式，它有两个谱参数，并构造了它的椭圆解。我们还研究了这些解的一些退化。

On elliptic solutions of the associative Yang-Baxter equation

We give a direct proof of the fact that elliptic solutions of the associative Yang-Baxter equation arise from appropriate spherical orders on an elliptic curve.

杨-巴克斯特映射的几何：二次曲线束和四有理映射

Geometry of Yang--Baxter maps: pencils of conics and quadrirational mappings

考虑双有理杨-巴克斯特映射（"杨-巴克斯特方程的集合理论解“）。一个双有理映射$(x,y)\mapsto(u,v)$称为四有理的，如果它的图也是一个双有理映射$(x,v)\mapsto(u,y)$的图。本文对$\CP^1\times\CP^1$上的四次有理映射进行了分类，并证明了它们都满足杨-巴克斯特方程.这些映射具有良好的几何解释的线性束的二次曲线，杨巴克斯特性质被解释为一个新的关联定理的射影几何的二次曲线。

Geometrization of trigonometric solutions of the associative and classical Yang-Baxter equations

We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang-Baxter equations. In the associative case the solutions come from symmetric spherical orders over the irreducible nodal curve of arithmetic genus $1$, while in the Lie case they come from spherical sheaves of Lie algebras over the same curve.

Torsion free sheaves on Weierstrass cubic curves and the classical Yang-Baxter equation

This work deals with an algebro-geometric theory of solutions of the classical Yang-Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstrass cubic curves.