查询词典 restricted lie algebra

Chapter 3: Take a further look at the development of the complete Lie algebra which conclude the simple Lie algebra.

第三章：展望一下包括单李代数的完备李代数的发展趋势。

And then the definition of simply complete Lie colour algebra and L self-homomorphism are given .A Lie colour algebra is simply complete if and only if it can not be decomposed .

然后给出了单完备李color代数的定义，并给出了一个李color代数是单完备的充要条件，即是不可分解的，同时引入了L的L自同态的定义。

A Lie group,called N-group,and its Lie algebra,calledN-algebra,are introduced for the structure analysis of the systems.

同时为便于进行系统的结构分析，引入一种称为N-群的李群及其李代数，N-代数。

Mathieu[17] discribe the form of Lie derivations on primitive ring whose charater is not 2 and which has no non-trivial idempotent. After that, Miers[18],Mathieu and Villena[19] also study Lie derivations on Von Neumann algebra and algebra.

Martindale[17]首先讨论了特征不等于2且含非平凡幂等元的本原环上的Lie导子的表达形式，随后Miers[18]，Mathien和Villena[19]也分别对VN代数，C~*-代数上的Lie导子进行了刻画。

In Reference [3], Cao and Tan described the automorphisms of Lie algebra of the strictly upper triangular matrices over R which is a maximal nilpotent subalgebra of the A_n type classical simple Lie algebra.

在参考文献[3]中，曹和谭把由所有严格上三角矩阵所构成的李代数的自同构问题已经完整的解决了，而这样的李代数恰好就是A_n型李代数的一个极大幂零子代数。

For the simplest interactive system of two particles with spin 1/2,the operator of Lie algebra can only realize the transition among the triplets, however, in order to realize the transition between the triplets and the singlet, the operators of Yangian must be involved, that is ,Yangian goes beyond Lie algebra in Quantum Mechanics.

对于最简单的两个-1/2的耦合系统，李代数生成元只能实现其自旋三重态之间的跃迁，而要实现三重态和单态之间的跃迁，必须由Yangian代数中的J 算子所引起，即 J 成为量子力学中超越李代数生成元的算子。

The solvable Lie algebra is corresponding to a cascade decomposition of the system and the semisimple Lie algebra is corresponding to a qasi-parallel decomposition such that the system has a parallel form of a cascade decomposition and a qasi-parallel decomposition.

任一李代数都可分解为一可解李代数与一半单李代数的半直和，可解李代数对应于系统的级联分解，半单李代数对应的是系统的准平行分解，将二者合并起来，就得到一般李群下的非线性系统的结构分解，这是一级联形式与一准平行形式的并联形式分解。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

This result is a generalization of the Chevalley basis in case a simply-laced complex simple Lie algebra. Meanwhile, it generalizes also the corresponding Chevalley forms in case affine Lie algebras and 2- extended affine Lie algebras.

该结果是simply-laced复半单李代数情形下Chevalley基的推广，同时也是仿射李代数和2-扩大仿射李代数的相应Chevalley结构形式的推广。

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。

We got alerted a couple of times while we were down south that HETs were on the way to bring us back up north because things were going to go hot again, but it was just rumors.

南下的途中我们不只一次得到警告说重型装备运输车将拉着我们重新北上，因为局势正在变得重新紧张起来，但这只是谣传。

It's the one where they find the ghost in the salt mine.

这一集是演他们在盐矿找到鬼