代数

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

Author uses the result of the periodicity theorem of complex Clifford algebra to obtain the irreducible representation of the odd\|degree complex Clifford algebra.

然而 ，周期性同构现象是复 Clifford代数中的一个重要特性，利用有关复 Clifford代数周期性定理的结果，本文作者得到了奇数次复 Clifford代数的不可约表

Secondly, for the spascial AF C* algebra-UHF algebra, I study the linear characterization of 2-local isometry on it: make use of the frame attribute, find the trace state of UHF algebra according to the one of matrix algebra and verify the 2-local isometry is linear.

充分利用UHF代数的结构特点，利用矩阵代数的迹态找到UHF代数的迹态，从而证明了2-局部等距的线性性质。

On Some Conclusions of the Isomorph ic Problem of L￣p Space and l￣q Space;2. A Proof of the Isomorph ism Theorem Between C_B-Algebra and Lu3-Algebra;3. Based on the BCK algebra homomorphism and isomorph, product is introduced and some qualities are given.

在BCK代数的同态同构基本定理基础上，引进了乘积并给出了它的性质，由此又进一步得到了关于模糊带算BCK代数乘积的同构定理，从而使模糊带算BCK代数的讨论更加深入。

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。

This paper mainly consider some basic theory of Frattini p-subalgebra of restricted Lie color algebra from four aspects.

首先，我们给出了关于限制李color代数的p-子代数，p-理想，p-幂零等几个基本定义，然后给出了几个重要定理，这是研究限制李color代数Frattini理论的重要依据。

This direction of research associates the graph in graph theory with the matrix in algebra by the matrix representation of a graph, then studies the algebraic property of graphs with the methods in graph theory and algebra.

该研究方向是通过图的矩阵表示将图论中的图与代数中的矩阵联系起来，再利用图论和代数方面的一些方法来研究图的代数性质。

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。

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。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。