Yang-Baxter方程与秩为$2$的自由群的特征有限单商群

杨-巴克斯特方程有限多置换解的特征

A characterization of finite multipermutation solutions of the Yang-Baxter equation

证明了杨-巴克斯特方程的有限非退化对合集理论解（X，r）是多置换解当且仅当其结构群G（X，r）允许左序或等价地是多无限循环的.

Drinfeld-Manin solutions of the Yang-Baxter equation coming from cube complexes

The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are higher-dimensional cube complexes solving the $D$-state Yang-Baxter equation for arbitrarily large $D$. More precisely, we introduce explicit constructions of cube complexes covered by products of $n$ trees and show that these cube complexes lead to new solutions of the Yang-Baxter equations.

Decomposition theorems for involutive solutions to the Yang-Baxter equation

Motivated by the proof of Rump of a conjecture of Gateva-Ivanova on the decomposability of square-free solutions to the Yang-Baxter equation, we present several other decomposability theorems based on the cycle structure of a certain permutation associated with the solution.

群、预群、括号、Yang-Baxter方程和$T$-结构上权为0的相对Rota-Baxter算子

Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures

本文研究群和李群上权为0的相对Rota-Baxter算子，并建立了其与预群、括号、Yang-Baxter方程集合论解及$T$-结构之间的显式关系。

Abelian fixed point free endomorphisms and the Yang-Baxter equation

We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an endomorphism gives rise to two non-degenerate solutions to the Yang-Baxter equation, solutions which are inverse to each other. We give concrete examples using dihedral, alternating, symmetric, and metacyclic groups.