上三角矩阵代数的交叉模和三阶上同调群

Crossed Modules and Third Cohomology of Triangular Lie Algebras

根据李代数的交叉模的定义,计算出上三角矩阵代数的交叉模等价类只有一个,相应的三阶上同调群平凡。

According to the definition of crossed modules of Lie algebras,it is proved that there is only one equivalent class of crossed modules of triangular Lie algebras,and that its third cohomology is trivial.