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For program (2), we can classify finite dimensional basic Hopf algebras of finite representation type completely now.

对于(2)，目前，我们已经给出了有限型的完整分类。

Let L and P be Lie color algebras and let M be a graded module over P, the crossed modules which make M as their kernal and P as their cokernal are considered. It is shown that under a suitable equivalent relation, there is a bijection between the set of the equivalent classes CML and the homogeneous components of degree zero of H~3.

从交叉模的定义出发，对于给定的Lie color代数L，P以及阶化P模M，考虑所有以M为核、以P为余核的L的交叉模，在这些交叉模之间定义了一个等价关系，由此得到交叉模的等价类集CML，证明了CML与三维上同调群H~3的零次齐次部分之间存在一一对应，从而可以利用三维上同调群对Lie color代数的交叉模进行分类。

We have classified all types of the solvable Lie algebras with nondegenerate invariant bilinear form.

我们给出了带有非退化不变对称双线性型的可解李代数的完全分类。

The relationships among Boolean algebra,set algebra,logic,and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers.

由于布尔代数、集合代数、逻辑学和二进制算术之间有内在的联系，所以布尔代数的理论在电子数字计算机的开发研制中是很关键的。

The relationships among Boolean algebra, set algebra, logic, and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers.

由于布尔代数，集合代数，逻辑学和二进制算术之间的内在联系，使得布尔代数的理论在电子计算机的发展中起到举足轻重的作用。

Keywords: The quantitative property of groups; Table Algebras; Cayley graphs

中文关键词：群的数量性质；表代数；Cayley图

At first, we give someelementary conception and properties of Novikov-Poisson Algebras, we elaborate on thegeneral conclusions about central extension and universal central extension in thechapter three.

我们首先给出了Novikov-Poisson代数的一些基本概念和性质，在第三章中详尽地阐述了中心扩张和泛中心扩张的一般结论。

Chapter 2 studies centralizers on J -subspace lattice algebras, and shows that such a centralizer is quasi-spatial implemented.

第一章介绍J -子空间格代数以及上述三类映射的基本概念和性质，并概括了本文的主要研究成果。

We prove every linear and local centralizer on J -subspace lattice algebras is a centralizer.

第三章研究J -子空间格代数的局部中心化子，证明J -子空间格代数的线性局部中心化子是中心化子。

The Schur_Weyl_Brauer duality relation between A,B,C, and D type of Liealgebras and their centralizer algebras, and its quantum version is emphasized.

特别强调了关于A，B，C，D型李代数及其量子情形与其中心代数之间的舒尔魏尔布劳双关性关系。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。