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Let D_(l+1)(R) be the orthogonal Lie algebra over a commutative ring R with 2 invertible and m_1 an l+ 1 upper triangular matrix. 设D_(l+1)(R)表示2为单位交换环R上的2(l+1)阶正交李代数。若记m_1是R上的l+1阶三角矩阵，而是D_(l+1)(R)可解子代数。
The main work of this paper is to study the RDS-type Lie Algebra. 本论文的主要工作就是对RDS型李代数进行研究。
In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings. 摘要本文研究了含幺可换环上一般线性李代数的子代数结构。
In terms of solvability of a matrix Lie algebra，new simple delay-independent stability criteria are presented. 从矩阵李代数可解性角度，推导出新的简单的时滞独立稳定性判据。
It is proved that the Frattini subalgebra of a complete Lie algebra with abelian nilpotent radical is the zero subalgebra. 证明了特征零代数闭域上的具有交换幂零根基的完备Lie代数的Fratini子代数为零。
Towers([1]) brought up a question :"If L is a Lie algebra all of whose nilpotent subalgebras are abelian , does L split over each of its ideals? 提出一个问题：“如果李代数L的所有幂零子代数都是交换子代数，那么L是否在它的每个理想上可分?
Based on a non-solvable matrix Lie algebra L, the derivations and automorphisms of L were studied by the multiplication operation of block matrix. 摘要以一类非可解矩阵李代数L为研究对象，利用分块矩阵的乘法运算，对L的导子及自同构进行了研究。
In this artical,we will expound only the application of group theory,particularly the Liegroup and Lie algebra,and topology to partical physics. 本文仅就纯粹数学中的群论,特别是李群和李代数以及拓扑学这两个分支在粒子物理学中的应用加以研究,以揭示数学在现代物理学中的重要作用。
This paper proves that any dipolarization in a real or complex semisimple Lie algebra is symmetric. Thus a complete answer to the open problem in reference[2] is gaven. 本文证明半单李代数上的任何双极化都是对称的，从而解决了金行壮二于1993年提出的一个待解的问题.;并给出了有关结果的一些应用
In section 2, we firstly give the relationship between the involutionary automorphism of Lie algebra and standard imbedding Lie algebra of Lie triple system. 其中包括李三系的子系、理想、单李三系、可解、半单、标准嵌入李代数以及李三系的同态等。
L_Z associated with finite-dimensional simpleLie algebras and affine Lie algebras of type k =1 over a commutative ring withidentity were defined by J. Hurley in 1969 and 1981 respectively, and theirideal structures were worked out there. Hurley在1969年与1981年分别对有限维复单李代数及k=1的仿射李代数L研究了相应的Chevalley代数L_R=RL_z的理想结构。
Abstract: This paper proves that any dipolarization in a real or complex semisimple Lie algebra is symmetric. Thus a complete answer to the open problem in reference[2] is gaven. 文摘:本文证明半单李代数上的任何双极化都是对称的，从而解决了金行壮二于1993年提出的一个待解的问题.;并给出了有关结果的一些应用
In this paper, the conclusion is that the intersection of lie subring of a Lie group is a Lie subring is obtained, moreover,it gives the Lie algebra of the Lie subring. 文章通过李子群的性质得出了李群的两个李子群的交依然是李子群的结论,进而得出这一李子群的李代数形式。
By using decomposition of exponential operators，the normal and antinormal ordering product of Boson exponential operators for SU(1，1) Lie algebra are given. 通过指数算符的分解，给出了SU(1，1)李代数玻色指数算符的正规和反正规乘积.
We take the coset space constructed by Lie algebra as the classical phase space for the molecular vibration to study its corresponding dynamical properties. 我们利用李代数的陪集方法,构造分子振动体系的经典相空间,探讨分子高激发振动的动力学特性。
Lie Groups, Lie Algebras, and Their Representation by V.S. 最重要的李群、李代数参考书;
Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra. 利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。
In this paper,the devivation algebra Dery of Lie algebra is given,y which is thd direct sum of a Heisenbery algebra H and an abelian &. It is proved that Dery id a simple complete Lie algebra. 文中给出了一个Heisenberg代数与一个交换Lie代数的直和的导子代数，证明了给出的导子代数为一个单完备Lie代数
In this paper,we first present two defining forms of Heisenberg Lie algebra. From these two forms,we determine the automorphism group Aut(H) of the(2n+1)-dimensional Heisenberg Lie algebra H.Moreover,some subgroups of Aut(H) are obtained. 首先给出了Heisenberg李代数的两种定义形式,由这两种定义形式,我们得到了(2n+1)维Heisenberg李代数的自同构群Aut(H);
He tried to varnish over the truth with a lie. 他试图用谎言来掩盖真相。