在线阅读 --自然科学版 2014年4期《一类可解李代数的结构》
一类可解李代数的结构--[在线阅读]
白瑞蒲1, 程荣1, 高瑞2
1. 河北大学 数学与计算机学院, 河北 保定 071002;
2. 沧州师范学院 数学系, 河北 沧州 061001
起止页码: 325--328页
DOI: 10.11826/j.issn.1000-5854.2014.04.001
摘要
可解李代数与幂零李代数在李代数结构中起着非常重要的作用.任意一个李代数L,都具有一个极大的可解理想与幂零理想,分别称之为L的可解根基RL)与幂零根基NL).因此,在李代数的结构研究中,可解李代数与幂零李代数的结构研究是必不可少的.研究了一类具有Filiform幂零根基的可解李代数的结构,证明了此类可解李代数是完备李代数,并且给出每个导子的具体表达式.

Structures of a Class of Solvable Lie Algebras
BAI Ruipu1, CHENG Rong1, GAO Rui2
1. College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002, China;
2. Department of Mathematics, Cangzhou Normal University, Hebei Cangzhou 061001, China
Abstract:
Solvable and nilpotent Lie algebras play an important role in the structure of Lie algebras.Every Lie algebra L possess a maximal solvable ideal and a maximal nilpotent ideal,which are called the radical R(L) and nilpotent radical N(L),respectively.The paper discusses a class of solvable Lie algebra L with Filiform nilpotent radical.It is proved that L is complete Lie algebra and gives an explicit expression of every derivation.

收稿日期: 2013-7-2
基金项目: 河北省自然科学基金(A2014201006)

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