线状李超代数Ln,m上的Yang-Baxter 方程

摘要

At first, we make a space direct sum decomposition of Ln,m over an algebraically closed field of characteristic zero, so the solutions of the Yang-Baxter equation of the filiform Lie superalgebras Ln,m were divided into several situations. We solve the Yang-Baxter equation in each case, then we obtain all the solutions of the Yang-Baxter equation of the filiform Lie superalgebras Ln,m in terms of the matrix form.%在特征零的代数闭域上,首先做出Ln,m 的一个空间的直和分解,从而将Ln,m 上的Yang-Baxter 方程的解分为若干情形。然后分别在每种情形下对Yang-Baxter 方程进行求解,进而得到了Ln,m 上的所有的Yang-Baxter方程的解的矩阵形式。