李代数

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

Early in the 1950s, in algebraic topology, the concept of graded Hopf algebras was derived from an axiomatization of the works of H. Hopf relating to topological properties of Lie groups. Hence the name,'Hopf algebra'.

50年代初，H.Hopf在研究李群的拓扑性质这一代数拓扑领域的理论工作中引入了分次Hopf代数的概念，"Hopf代数"由此而得名。

Finite commutative group; Symmetric bicharacter; Lie color superalgebra ; Left color symmetric algebra ; Left color symmetric structure

基础科学，数学，代数、数论、组合理论有限交换群；对称双特征标；着色李超代数；左着色对称代数；左着色对称结构

Based on LML theory frame and its algebraic model, geometric model and learning axiom systems, going for further study, this paper presented orbits generated algorithm of learning subspace in LML and applied it to corresponding examples, such as classify of human, chemical composition of wine and eight data sets including Soybean-Large, etc.

本文在李群机器学习的理论框架上，以李群机器学习的代数模型、几何模型、学习的公理系统为基础作进一步研究，给出了李群机器学习的学习子空间轨道生成算法，将该算法应用于人群分类，葡萄酒化学成分分类以及大豆等八个专用数据集的分类，取得了满意的结果。

First,we give some basic concepts of restricted Lie color algebra,for example,p-subalgebra,p-idea and p-nilpotent Lie color algebra.

然后，我们得到限制李color代数的Frattini子代数和Frattini p-子代数的基本性质并证得可解限制李color代数的Frattini子代数和Frattini p-子代数是两个幂零理想。

Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.

在任意特征域上，从∧(2，2)和它的特殊导子的子空间的多项式代数出发，构造了一类Weyl型结合超代数和一类Weyl型李超代数，进而给出并证明了它们为单的充要条件。

We introduce the notion of characteristic pairs and give the definition of dual characteristic pairs of Dirac structures on Lie bialgebroids. Using the dual characteristic pairs, we give the if and only if conditions for which a maximally isotropic subbundle of the double of a Lie bialgebroid is a Dirac structure.

本文在李双代数胚上，引入了Dirac结构的特征对并给出对偶特征对的概念，利用对偶特征对，给出李双代数胚double的极大迷向子丛是Dirac结构的充要条件；其次，分别利用特征对与对偶特征对，将可约Dirac结构分为第一类可约与第二类可约，在此基础上，建立Poisson流形的两类对应约化定理。

Let 〓 be a finite-dimensional Z-graded Lie superalgebra.Weprove that if L has a non-degenerate trace form then s=r.Using the result,weobtain that the Killing forms of Lie superalgebras of Cartan type are degenerate.

本文得出如果有限维单Z-阶化李超代数L=〓具有非退化迹型〓，则s=r，由此可推出Cartan型李超代数的killing型是退化的。

In this paper, we mainly study Lie color algebras; discuss the algebraical structure of Lie color algebras.

本文的主要目的就是研究着色李超代数，对这种代数结构进行一系列讨论。

In this paper, we try to discuss the classification of low dimensional Lie super algebras.

本文主要讨论了特征p=0的代数闭域上的低维李超双代数的分类问题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。