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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.

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。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

In section 2 ,if one Lie colour algebra can be decomposed to direct sum of two ideas ,the same as the center.And when the center is zero , the derivation and the inner derivation can be also decomposed .Lie colour algebra L is complete if and only if its two ideas are both complete .

第二部分首先讨论了若李color代数L可以分解为两个理想的直和，则中心也可以分解为两个理想的直和，而且当中心为零时导子和内导子也有同样的理想直和分解，并且L完备的充要条件是两个理想都完备。

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。

A virtue ethicist, however, would focus less on lying in any particular instance and instead consider what a decision to tell a lie or not tell a lie said about one's character and moral behavior.

美德伦理学家，但是，将集中在任何特定情况下不说谎，而是考虑如何决定撒谎或不撒谎说，大约一个人的性格和道德的行为。

Considering the vehicular SG cruise integrating model under braking condition influenced by some factors of nonlinearity, time-delay and the disturbance, a new nonlinear SMITH predictor is designed to compensate the time delays of control variable in advance. Furthermore, with the resort of pure delay operator, extension of the Lie derivative and the Lie bracket, some issues of SISO nonlinear system with time delays in state variable are resolved, which cover the input-output linearization, invertability of coordinate transformation and the disturbance decoupling problem.the staged transformation and design technique, the vehicle deceleration tracking control and the SG cruise disturbance decoupling control under braking condition are carried out effectively using proposed control method.

在建立制动工况下车辆走-停巡航系统集成模型基础上，针对其非线性、时滞特性以及目标车减速度干扰的影响，提出一种改进的非线性SMITH预估补偿方法，以消除控制变量时滞，并结合时滞算子、扩展李导数和扩展李括号方法，研究并解决了SISO状态变量时滞非线性系统的输入输出线性化、坐标变换的可逆性以及输出干扰解耦问题，实现了SISO时滞非线性系统的综合控制。

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。

A preious population-based surey found a linear association between the number of lie births and chronic LBP, een after adjusting for age, BMI, smoking, and car ownership as an indicator of social class in both men and women. Also in pregnant women, the number of lie births was associated with LBP.

以前有一项人口调查发现：无论男性或女性，即使经过了包括年龄、BMI及社会阶层指示的汽车拥有情况等因素的调整后，仍显示在子女数目与慢性LBP间有线性相关关系。

Now, I have become hypocritical, I can not say I do not want the truth, just because selfish fear of injury ... in his own set of barriers in life with a mask ... Once I am naive, sometimes silly, no matter small or big, my friends are like lie to me, use me, have a boyfriend cheated on me with other girls contacts, since the occurrence of such incident, I can not believe that any , even I dare not touch it, I hate it when they lie ....

现在的我变得虚伪，我不敢也不愿说出我的真心话，只因为自私的害怕自己受伤…在自己设的屏障里带着面具生活…曾经的我很天真，有时还傻傻的，不管小事或大事，身边的朋友都喜欢骗我，利用我，曾经的男朋友背着我和其它女孩交往，自从发生这些事后，我不敢相信任何人，甚至我不敢接触人们，我讨厌她们说谎…。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。