一类具有特定幂零根基的可解李代数

Class of Solvable Lie Algebras with a Given Nilradical

讨论了一类具有二维中心的三步幂零李代数的一些结构性质,研究了以这类幂零李代数为幂零根基的不可分解的可解李代数,确定了该类可解李代数的维数,并具体构造出复数域上其中一类6维的可解李代数.

In this paper, we have discussed a 3-step nilpotent Lie algebra with a two dimensional center and studyled a class of indecomposable solvable Lie algebras which nilradieal is the nilpotent Lie algebra. We have determined the dimension of the solvable Lie algebras and constructed a class of the solvable Lie algebras of 6 dimension over complex field.