lie algebra

We also discuss a natural involution of necklace Lie algebra.

我们还讨论了由重箭图自然自同构导出的李代数的一个自然的对合。

This paper characterizes the minimal ideals of finite dimensional quadratic Lie algebras over the complex field and gives an optimistic lower bound for the dimension of the space of invariant symmetric bilinear forms on a quadratic Lie algebra by means of the number of linearly independent minimal ideals.

刻划了复数域上有限维二次李代数的极小理想，并用线性无关极小理论的个数给出了这类李代数上对称不变双线性型所成空间维数的一个最好下界刻划。

The third chapter main research is two new high-dimensional Lie algebra and its application.

第三章主要研究的是两个新的高维的Lie代数及其应用.

Let n be the nilpotent Lie algebra consisting of all strictly upper triangular ( n+ 1)×( n+ 1) matrices over an integral domain R of characteristic 2.The aim of this paper is to give an explicit description of the automorphism group of the Lie algebra n.

设n是特征为2的整环上由所有严格上三角（n+1）×（n+1）矩阵构成的李代数。本文的目的是确定李代数n的自同构群。

the second, fourth and sixth order fluctuations have been discussed by making use of su ( 2) lie algebra. on the basis of higher order uncertainty relation, the definition of higher order squeezing for the fluctuations of angular momentum has been put forward.

利用SU（2）李代数讨论了原子相干态中角动量的二阶、四阶和六阶涨落，并在高阶不确定关系基础上提出了角动量高阶压缩的定义。

In this thesis we will complete the necklace lie algebra from a special quiver.

本文从一类特殊的箭图出发构造项链李代数.

We completely determined the structure of Derg of the 3-solvable non-degenerate Lie Algebra, g.

进而给出了三次可解型非退化李代数的一个等价条件，并且详细地刻画了它的导子李代数的结构。

A New Kind of Indefinite Type Kac-Moody Lie Algebra

一类不定型Kac-Moody李代数

We first discuss the classification of complex simple Lie triple systems using the classification of finite order automorphisms for each complex simple Lie algebra given by Kac.

第三部分，在Lister关于李三系的分类定理的基础上，利用Kac对复单李代数的有限阶自同构的分类对复数域上的单李三系进行分类。

The Killing Model and Ideal of ( p, q) form Lorentz Lie Algebra Over Rings

环上（p，q）型Lorentz李代数的Killing型与理想

based on the lie algebra that describes the symmetries, it is proved in this dissertation that a sufficiently large class of control hamiltonians can be provided by the universal enveloping algebra of the lie algebra, on which the quantum mechanical control systems can be modelled.

基于描述量子力学系统对称性的李代数结构，本文证明该李代数的泛包络代数提供了足够大的一类控制哈密顿量，因而可以在其上建立量子力学控制系统的模型。

Integrable Modules of Affine Kac& Moody Lie Algebra

仿型Kac&Moody李代数的可积模

nonlinear optics of the electrostatic accelerator tubes-third order lie map dynamical lie algebra method for nonlinear triatomic molecule potential energy surface

Lie代数方法及其在静电加速管像差分析中的应用&三级近似非线型三原子分子势能面的Lie代数方法

Y-type Lie algebras of the infinite dimensional matrix Lie algebra on complex field

复数域上无限维矩阵李代数的y-型李代数

especially to the finite dimensional lie algebra is a very important work.

特别是对有限维李代数结构和分类的研究，是一个非常关键并且具有重要意义的问题。

Dynamical Lie Algebra Method for Highly Excited Vibrational State of Quasi-linear Tetraatomic Molecules

准线型四原子分子高激发振动能级的动力学李代数方法

The authors, discuss the product Lie group's Lie algebra.

本文还讨论了乘积李群的李代数形式.

let u ( d) be the universal enveloping algebra of the lie algebra spanned by d.

令U（D）是D的泛包络代数。

fourier transforms of invariant functions on finite reductive lie algebra

有限可约化李代数上不变量函数的傅立叶变换

Central Extensions of the Lie Algebra G 2 over a Field Characteristic 2

特征2李代数G2的中心扩张

SU ( 1, 1) Lie Algebra of Nonlinear Nonharmonic Oscillator

非线性非谐振子的SU（1，1）Lie代数

structure of a class of finite dimensional power zero lie algebra

一类有限维幂零李代数的结构

A left-symmetric algebra decides uniquely its sub-adjacent Lie algebra up to isomorphism ( [ 7], Proposition 12). A natural question is: Is every Lie algebra the sub-adjacent Lie algebra of some left-symmetric algebra?

一个左对称代数在同构意义下唯一确定其邻接Lie代数（〔7〕命题12）.一个自然的问题为：是否每个Lie代数都是左对称代数的邻接Lie代数呢？

In this paper, we extend the concept of quantum Lie algebra to two-parameter case.

本文把量子李代数的概念推广到了双参数的情形.

In this paper, the author generalizes the level two representation [ 11] of the Kac-Moody algebra A1 ( 1) to the Toroidal case, and gives a class of irreducible modules for the A1 Toroidal Lie algebra.

本文将Kac-Moody代数A1（1）的二阶表示理论[11]推广到Toroidal李代数的情形.并给出了A1型Toroidal李代数的一类不可约表示。

constructing potential energy surface of tetratomic molecules using lie algebra

用李代数方法构造四原子分子的势能面

The electromagnetism in vacuo and Lie algebra of the Lorentz group

真空中的电磁场与洛仑兹群的李代数

regular element of a lie algebra

李代数的正则元

The seidel third-order aberration coefficients of a thick lens imaging system are derived analytically with the aid of Lie algebra and optical symplectic map.

借助于李代数和辛映射推导出厚透镜成象系统的Seidel三级象差系数的解析公式。

Induced by the symplectic structure, we have obtained the Poisson bracket and the Lie algebra for the conservative quantities with respect to the Poisson bracket.

我们由其上的辛结构定义了其上的Poisson括号，并求出了在这个括号意义下，守恒量所构成的李代数。