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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。

First, we give the definition of Lie color superalgebras using the symmetric bicharacter on a finite commutative group, and also we introduce some fundamental notions about Lie color superalgebras.

首先根据有限交换群上对称双特征标的概念，给出着色李超代数的定义，并介绍关于着色李超代数的一些基本概念与基础知识。

Not only baroclinic instability and conditional symmetry instability lie in the middle-low level, but also lie in the middle-upper level of DMMCS. At the west of DMMCS, there lies negative MPV2 column.

深湿对流系统的中低层不仅有对流不稳定，而且还有斜压不稳定、条件对称不稳定，而中高层必须有湿斜压不稳定和条件对称不稳定。

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。

Absolute freedom; an absolute dimwit ; a downright lie; out-and-out mayhem; an out-and-out lie; a rank outsider; many right-down vices; got the job through sheer persistence; sheer stupi di ty.

彻底的自由；彻头彻尾的傻瓜；彻底的谎言；完完全全的故意伤害；彻底的谎言；十足的失败者；许多彻底的堕落；完全通过坚持才得到了这份工作；十足的愚蠢。

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。

The differences of the various schools of thoughts and their exponents during the period from pre-Qin times to the early years of the Han Dynast do not lie in their advocacies, for they are all autocracism affirmers; nor do they lie in their historical conditions, for they all regard that autocracism should be conducted under any historical conditions, i.

中国诸子百家之不同，不在于是否主张专制，因为他们都是肯定专制的专制主义论者；也不在于主张在何种历史条件下应该专制，因为他们都认为专制在任何历史条件下都是应该的，他们都是永恒的超历史的专制主义论者。

In another word, if we want to make an area have notable effect of agglomeration, the key does not lie in the size of advantage of agglomeration, but lie in the factors of elasticity of substitution of industry agglomeration.

或者说，要使一个地区有明显的集聚效果，关键不在于该地区集聚优势到底有多大，在于它替代其他地区的能力，进一步说，是在于集聚的替代弹性的影响因素。

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。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。