李代数

As the center or the Algebra subalgebra of a algebra plays an important role in reducing the number of state variables, the cartan subalgebra is a maximum Abelian subalgebra of an algebra, so it can be a powerful tool for the structure simplification of control systems.

由于代数的中心，或交换子代数在系统的变量降低方面具有重要作用，而Cartan子代数是李代数的极大交换子代数，因而它能成为简化系统结构的有力工具，第二部分利用向量场的积分曲线所定义的映射，构造出一个S—坐标，在该坐标下任一向量场都有一个标准的表示方法，一种无穷级数表示方法。

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

Based on the filtered Lie algebra of the universal enveloping algebra, the algebraic structure of projected subsystems are studied. It is proved that they have simple decompositions, and the construction of the representations is given as well as the corresponding criterion for project limit controllability.

基于泛包络代数的滤李代数结构，研究了投影子系统的代数结构，证明它们具有简单的分解形式，并给出了它们的表示的构造方法和投影极限能控性的判别定理。

Currently Lie group methods are of huge value and they are popular abroad and lead to the computation of matrix exponential to be a hot topic.

近年来在国外流行的李群方法，由于具有重大的科学价值，在李群算法发展的需求下，李群、李代数里的指数计算，也成为了研究的热点。

In section 2.2,we prove that if the set of arrows in a quiver is not empty,then NQ is not semisimple.We construct the nonsovable subalgebra of NQ when there is no less than one circle whose length is bigger than one ,and there is no loop in quiver Q,thus leads to a conclusion that NQ is nonsovable .

我们还对只有一个单循环和一个单循环及若干单箭头的箭图，给出了其项链李代数的某些中心元素的具体形式，在2.2节中，我们对非平凡图，即当箭图中有箭头时，利用H中的元素证明了N_Q不是半单纯李代数。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Prof. Hsio-Fu Tuan,a member of Academia Sinica and eminent mathematician in China, has made outstanding contributions in the theory of modular representations of finite groups, algebraic Lie algebras and the study of p-groups,especially their "Anzanl" theorems.

从30年代末开始，他在有限P群、有限群模表示论和代数李代数方面做出了一系列重要贡献，得到了被冠以布饶尔－段－斯坦顿原则，布饶尔－段指标块分离原则，布饶尔－段定理等名称的突出成就，在中国开辟了代数群论等研究领域并形成了富有特色的研究群体。

Through coupling of computational car course 5 rank the Li Dai of the model is counted, got Li Dai counts the verdict of full order, make clear 5 rank the system that the model is strong coupling of course of a car, alternate through coordinate the system cannot solve Ou only.

通过计算车轨耦合五阶模型的李代数，得到了李代数满秩的结论，表明五阶模型是一个车轨强耦合的系统，仅通过坐标变换系统无法解耦。

Lie superalgebras are the generalization of Lie algebras, and they are closely related with physics.

李超代数是李代数的一种推广，这一数学概念有着很强的物理背景。

This thesis consists of two parts,part I:Complete Lie algebras and part II:Sym-metric self-dual Lie algebras...

本文由两部分构成：第一部分：完备李代数；第二部分：对称自对偶李代数。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。