本文探讨项链李代数的结构及性质。
We study the structure and properties of a necklace Lie algebra.
元微分算子代数的导子李代数结构。
Lie algebras of derivations of n-differential operator algebra.
结论是交换超算符方法的理论基础是李代数。
The conclusion is that the theoretical foundation of commutative hyper-operator method is Lie algebra.
提出一种李代数方法描述分子反应碰撞问题。
The dynamical Lie algebraic method for describing the reactive collisions is presented.
本文给出完备李群与完备李代数的某些关系。
In this paper, we will investigate relations between complete Lie groups and complete Lie algebras.
本文把量子李代数的概念推广到了双参数的情形。
In this paper, we extend the concept of quantum Lie algebra to two-parameter case.
本论文的主要工作就是对rds型李代数进行研究。
The main work of this paper is to study the RDS-type Lie Algebra.
应用李代数方法讨论了非简谐振子激光激发的统计性质。
The statistical properties of non-harmonic oscillators' laser excitation are discussed by using Lie algebraic method.
近年来李代数方法成为研究分子势能面的强有力的工具。
In recent years Lie algebraic method has become a powerful tool to study the PES of molecules.
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 this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings.
代数技巧；李群和李代数；离散数学；量子群；随机方法。
Algebraic Techniques; Lie Groups and Lie Algebras; Discrete Mathematics; Quantum Groups; Stochastic Methods.
这是由SU（2）李代数生成元之间的反对易关系导致的。
This is due to the anticommunication relation between the SU(2) generators.
本篇文章主要讨论了李代数胚联络以及它的一些性质和应用。
In this paper, we will mainly discuss the Lie Algebroid connection including some properties and applications of it.
以磁四极透镜为例，用李代数方法分析强流脉冲的非线性传输。
Nonlinear transport of intense charged particle beams is analyzed with Lie algebraic methods.
代数群的连通正规闭子群与李代数的理想之间有很特殊的关系。
There are particular relations between the closed connected normal subgroups of algebraic groups and the ideals of Lie Algebras.
证明了广义限制李代数意义下的诱导模成为(？)-模范畴对象。
We prove that as a generalized restricted Lie algebra, the induced modules of s (m; n) are objects of the (?) -module category.
动力学李代数方法在研究原子分子碰撞问题中是一种很重要的方法。
The dynamical Lie algebraic method is used for the description of statistical mechanics of the atom-diatom collision.
在适当地选取了半单李代数的根系之后，就可算出初等表示权的标积。
When the set of roots for a semi-simple Lie algebra have been selected appropriately, the scalar product of the weights of the elementary representation can be calculated.
本文用生成元和定义关系的方法，对每个可解可补李代数给出一个定义矩阵。
A defining matrix is given for the solvable and complemental Lie algebras with a generator relation method.
结果表明代数动力学方法对于具有非半单李代数结构的线性动力系统仍然适用。
It has also been shown that the algebraic dynamics might be generalized from the linear dynamic system with a semi-simple Lie algebra to that with a general Lie algebra.
基于近代微分几何理论与李代数之上的非线性控制理论形成了一新的理论分支。
Based on modern differential geometric approach and Lie algebra, nonlinear control theory has formed a new theoretical branch.
本文应用李代数嵌入法严格地处理相互作用玻色子模型(IBM - 1型)。
This article treats the interacting Boson model (IBM-1) by the embedding theory of Liesubagbra.
在有单位元的交换环上，可应用生成元和定义关系的方法给出仿型李代数的定义。
On commutative ring with the identity, the definition of affine Lie algebras was given by applying the means of generator and defining relation.
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。
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.
李代数的抽象理论中很多重要的概念都来源于经典群论，完备李代数便是一个例子。
Many of important concepts in the theory of abstract Lie algebras come from classical theory of groups, for example, complete Lie algebras is a generalization of complete groups.
利用李代数方法给出了含时库仑势量子体系的严格解，并指出了该方法的适用条件。
By use of Lie algebraic method, the exact solution of a quantum system with time-dependent Coulmb potential was obtained, and the suitable condition of the method was pointed out.
将李群李代数理论成功地拓展应用于空间柔性机构系统的分析，验证了该方法的有效性。
The Lie groups and Lie algebras is successfully extended to study the mechanical system with spatial compliant links.
本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系。
In this paper, we apply the concept of the generalized restricted Lie algebra to study the relation of the integral and central extensions of a Lie algebra with a triangular decomposition.
最后一部分中，我们讨论左对称代数和李代数上的左对称结构在着色李超代数中进一步的推广。
In the last part, we further generalize left symmetric algebra and left symmetric structure on Lie algebras into Lie color algebras.
在量子光学、凝聚态物理、原子分子物理中存在许多典型的具有三生成元李代数结构的量子系统或模型。
There exist a number of typical systems and models which possess the three generator Lie algebraic structure in quantum optics, atomic and molecular physics and condensed matter physics.
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