查询词典 Cartan subalgebra

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。

Then we study the typical property of theirs form the starting of nature and constitute of the two types of Lie algebra, and we calculated separately their dimension, center, commutator algebra, Killing type, Cartan subalgebra, structure formula, root system, and so on.

本文主要研究了两类典型的李代数即李代数so*(2n)和g*，首先介绍了一些李代数的基本知识，并且给出了这两类李代数的组成结构，然后从这两类李代数的本质构成出发，研究它们的一些典型性质，分别讨论了它们的维数，中心，换位子代数，Killing型，Cartan子代数，结构公式，根系等。

Section 1 uses the cartan subalgebra to simplify the structure of systems.

第一部分利用Cartan子代数简化系统的结构。

Let g be a finite dimensional complex semisimple Lie algebra with the Cartan subalgebra h.

令g为一个有限维的复半单李代数，而h是g的Cartan子李代数。

We prove that any irreduciblesymmetric self-dual Lie algebra 〓 whose Cartan subalgebra consists of semi-simpleelements is in one of the following classes:(1)〓 is simple;(2)〓 is 1-dimensional;(3)〓is solvable.

第五节讨论Cartan子代数由半单元构成的对称自对偶李代数的结构，证明了不可约对称自对偶李代数g如果它的Cartan子代数由半单元构成，那么它只能是下列情形之一：（1）g为单李代数；（2）g是1维的；（3）g是可解的。

In this paper, we first solved the characterization of Lie ideal in aσ-weakly closed triangular subalgebra A of an AF vN algebra B with cartan subalgebra D.

本文首先描述了AF von Neumann代数B中对角为Cartan子代数D的σ-弱闭的三角子代数A的σ-弱闭Lie理想。

Theorem C: The commutator algebra of so *(2 n ) is its own, and the commutator algebra ofand the commutator algebra of Theorem D: The Cartan subalgebra ofand the Cartan subalgebra of Theorem E: The structural formula of

定理C so *(2 n )的换位子代数就是其本身， g *(2 n， S ， C )的换位子代数为g *(2 n + 1， S ， C)的换位子代数为定理D so *(2 n )和g *(2 n ， S ， C )的Cartan子代数是定理E so *(2 n )和g * m， S ，(来源：AB78C论文网www.abclunwen.comC 的结构公式都是来源：A6bBCe9论文网www.abclunwen.com

In Kac-Moody algebra, if the given element is a real root vector or in Cartari subalgebra, there exists an element such that they can generate the algebra.

在Kac-Moody代数中，如果预先给定的元素属于Cartan子代数或者是实根向量，能够找到它的配对生成元。

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。