半单代数

Next, we discuss the relations between left quasi-dual bimodules and left dual-bimodules, we obtain that a left quasi-dual bimodule is a left dual bimodule if it satisfies one of the following conditions: sM is minimal injective and MR is a M-minimal injective kasch-module; MR is a M-minimal injective kasch-module and for any two ideals LI and L2 ofSS rM(L1 n L2)-rw(L1)+rM(I2); sM is minimal injective and for any two submodules A and B of MR,Lastly, we applicate the quasi-duality on smash product algebra R#H, and obtain an answer of the semiprime problem, i.e., let H be a finite-dimensional semisimple Hopf algebra and R be an H-module algebra, if R is left quasi-dual and semiprime, then R#H is semiprime.

我们得到：一个左拟对偶双边模如果满足下列条件之一，则它将成为一个左对偶双边模：_sM是单内射的并且M_R是一个M-单内射kasch-模；M_R是一个M-单内射kasch-模并且对_sS的任意两个理想，有r_M(L_1∩L_2)=r_M(L_1)+r_M(L_2)；_sM是单内射的且对M_R的任意两个子模，有l_s=l_s+l_s。2 在第2.3节中我们将拟对偶性应用于smash积代数R#H，部分解决了半素问题。

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。

As well as we introduce some property of Killing form. Finally, we use Killing form to decide if YD-Lie algebras are semisimple.

则称为L的Killing型，以及给出了Killing型的性质，最后用Killing型去判断半单点YD-李代数。

In particular the semi-linear transformation of a single, the study of the Lie algebra structure, and the existence of classification play an important role.

特别是半单的线性变换，对研究李代数的结构、存在与分类，起到重要作用。

In section 2.2,we prove that if the set of arrows in a quiver is not empty,then NQ is not semisimple.We construct the nonsovable subalgebra of NQ when there is no less than one circle whose length is bigger than one ,and there is no loop in quiver Q,thus leads to a conclusion that NQ is nonsovable .

我们还对只有一个单循环和一个单循环及若干单箭头的箭图，给出了其项链李代数的某些中心元素的具体形式，在2.2节中，我们对非平凡图，即当箭图中有箭头时，利用H中的元素证明了N_Q不是半单纯李代数。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

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。