一类具有特殊6维幂零根基的7维可解李代数

可解李代数的分类问题是李代数中未完全解决的一个基本问题.主要探讨了一类特殊的6维幂零李代数的一些结构性质,找到了这类幂零李代数的生成元,并且计算了这类幂零李代数的导子.然后,利用这类幂零李代数的导子,构造出在复数域上以这类特殊的6维幂零李代数为幂零根基的7维不可分解的可解李代数.在构造的过程中,给出了一种判断具有这个相同的幂零根基的2个可解李代数同构的条件,并利用这种方法消去了一些重复出现的情况.由于情况比较复杂,主要列举了几种比较有针对性的情况作为例子,得到了一部分以这类幂零李代数为根基的7维的可解李代数

Solvable Lie algebra of seven dimensional with a special six dimensional nilpotent radical

The classification of solvable Lie algebra is a basic problem in Lie algebra which have not been solved now.In this paper we discuss the structure of a special class of six dimensional nilpotent Lie algebra.We find the minimal generator of this kind of nilpotent Lie algebra and compute the derivations of the nilpotent Lie algebra.Then we construct the seven dimensional solvable Lie algebra with this six dimensional nilpotent Lie algebra according to the derivations of the nilpotent Lie algebra.In the process of constructing seven dimensional solvable Lie algebra, we give a condition for the isomorphism of Lie algebra which have the same nilradical.We also eliminate the repeated emergences by isomorphic relations.Because the problem is too complicated,we list some important cases as examples and get some special kinds of seven dimensional solvable Lie algebras at the end of the paper.