一类五维李代数的交叉模

Crossed Modules of a Class of Five-Dimensional Lie Algebras

文[1]主要研究了四维不可解李代数的交叉模的等价类集和三阶相对上同调群。在此基础上,本文研究了一类五维李代数的交叉模的性质,并确定出其等价类的条件,从而证明了这类五维李代数的三阶相对上同调群不是平凡的。

The set of equivalence classes of crossed modules of four-dimensional unsolvable Lie algebras and the third relative cohomology groups were studied in[1].Based on this work,the present paper will study the crossed modules of a certain five-dimensional Lie algebra and determine the condition of its equivalent class.Furthermore,it is shown that the third relative cohomology group of the five-dimensional Lie algebra is not trivial.