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In [3], Professor Wang Xian-dong discussed the evaluation modules of Loop algebras of Lie algebras with a triangular decomposition; particularly, irreducibility of the tensor product of finitely many such modules was partially determined.

在[3]中，王宪栋教授讨论了可三角分解李代数其Loop代数的赋值模；特别值得一提的是，在一定程度上确定了有限多个赋值模其张量积的不可约性。

Firstly, we define the Killing form over any finite dimensional Hopf algebras using the adjoint action, then we investigate the fundamental properties of the Killing form, and obtain a decomposition of Hopf algebras under the adjoint action.

首先，利用Hopf代数的伴随作用定义了有限维Hopf代数上的Killing型，并讨论了Killing型的基本性质，得到了Hopf代数上的伴随表示分解式。

In order to discuss the structure of operator algebras, in recent years, a lot of schol-ars both here and abroad have focused on linear mappings of operator algebras andhave introduced more and more new methods.

为了进一步探讨算子代数的结构，近年来，国内外许多学者对算子代数上的线性映射进行了深入研究，并不断提出新的思路。

Yu introduced in 1997 the localization Roe algebras , and shown that, to attack the Coarse Baum-Connes Conjecture, it suffices to prove that the local index map is an isomorphism from the coarse K-homology to the K-theory of the localization Roe algebras.

Yu受热方程方法的启发，引入局部化Roe代数，把粗Baum-Connes猜测的证明归结为证明从粗化K-同调群到局部化Roe代数的K-理论群的局部指标映射为同构。

By using Jordan-Hlder type theorem of table algebras, we prove that table algebras satisfying nilpotent extension condition are nilpotent, which does not correspond to extension problems of nilpotent groups exactly.

本文研究了幂零表代数的一个有趣的性质，利用表代数的Jorda-Hlder型定理，证明了表代数满足幂零被幂零扩张仍是幂零的，但有限幂零群没有这样的扩张。

Furthermore,we show that there exists a 1-1 correspondence between the set ofthese CN Lie algebras and the set of nilpotent Lie algebras of maximal ranks.

第三节引进了CN李代数和CS李代数的概念，证明了极大秩幂零李代数和Heisen-berg代数均为CN李代数。

We discuss the completely tr-rank nonincreasing linear maps on finite vN algebras and prove that a unital self-adjoint and surjective linear map on finite vN algebras is completely tr-rank preserving if and only if it is a spatial 〓-automorphism that leaves the central elements fixed.

我们刻画了有限vN代数上完全迹秩不增的线性映射；也证明了有限vN代数上保单位元的自伴线性满射完全保迹秩当且仅当它是空间〓-自同构且限制到中心上是恒等映射。

The class of non-selfadjoint operator algebras is an important domain in operator algebras reaserching.

非自伴算子代数是算子代数中一个重要的研究领域，而套代数是一类最重要的非自伴算子代数。

The representation type of algebras is one of the main themes of representation theory of algebras.

决定代数的表示型是代数表示论的主要课题之一。

In recent years,representation theory of finite-dimensional algebras has intersected and permeated through Lie algebras,which is one of the important features.

与李代数的交叉与渗透是近年来有限维代数表示理论发展的重要特点之一。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。