对称代数

最后一部分中，我们讨论左对称代数和李代数上的左对称结构在着色李超代数中进一步的推广。

In the last part , we further generalize left symmetric algebra and left symmetric structure on Lie algebras into Lie color algebras .

标度整体最小二乘问题及对称代数Riccati方程的扰动分析及条件数

Perturbation Analysis and Condition Numbers of Scaled Total Least Squares Problems and Symmetric Algebraic Riccati Equations

最后，我们给出求解传输理论中非对称代数Riccati方程的修改的简单迭代法和修改的牛顿法。

Finally , we propose a modified simple iterative method and a modified Newton method for nonsymmetric algebraic Riccati equations arising in transport theory .

具有Virasoro型的无穷维对称代数的群不变模型

Invariant Models with the Infinitely Dimensional Virasoro-type symmetry Algebra

但对一类特殊的非对称代数Riccati方程，我们运用位移变换可将其转换成一个新的Riccati方程，使得新方程的四个常数矩阵组成的矩阵K为非奇异矩阵。

For a special class of nonsymmetric algebraic Riccati equation , we use shift technique to transform the original Riccati equation into a new Riccati equation , making K a non-singular matrix .

一个左对称代数在同构意义下唯一确定其邻接Lie代数（〔7〕命题12）.一个自然的问题为：是否每个Lie代数都是左对称代数的邻接Lie代数呢？

A left-symmetric algebra decides uniquely its sub-adjacent Lie algebra up to isomorphism ( [ 7 ] , Proposition 12 ) . A natural question is : Is every Lie algebra the sub-adjacent Lie algebra of some left-symmetric algebra ?

超对称代数GSU2的研究Ⅰ.不可约表示.C&G系数

Studying to the supper-symmetric algebra gsu_2 I. irreducible representations and C-G coefficient

非对称代数Riccati方程出现在许多科学计算和工程应用问题中，该方程的数值求解问题也就成为了科学研究的热点之一。

Nonsymmetric algebraic Riccati equation appears in many areas of scientific computing and engineering applications , the Numerical Methods for solving the equation become the focus of scientific research .

超对称代数GSU2的研究Ⅱ.Racah系数和不可约张量算符

STUDYING TO SUPER-SYMMETRIC ALGEBRA GSU_2 ⅱ . Racah Coefficient and irreducible tensor operator

本文根据矩阵的Jordan标准形建立矩阵的交换代数的构造方法，在此基础上导出双线性系统的对称代数，并给出寻找一般非线性系统的对称群的一种途径。

In this paper the construction of commutative algebras for a matrix is established according to its Jordan canonical matrix . From this the symmetry algebra of a bilinear system is derived and a way of finding the symmetry group for a nonlinear system is presented .

对一般形式的非对称代数Riccati方程，当方程的四个常数矩阵组成的矩阵K为非奇异M-矩阵或不可约奇异M-矩阵时，已经被证实其最小非负解存在。

Let K be an M-matrix which is composed of four coefficient matrices of nonsymmetric algebraic Riccati equations . When K is a nonsingular M-matrix or irreducible singular M-matrix , it has been confirmed that the general form of nonsymmetric algebraic Riccati equation has the minimal nonnegative solution .

左对称代数的扩张及其应用

The extensions of left-symmetric algebras and their applications

双线性系统：对称代数构造

Bilinear Systems : Construction of Symmetry Algebras

左对称代数的若干性质

Some properties of left - symmetric Algebras

左对称代数（Ⅱ）

On left - symmetric algebras (ⅱ)

左对称代数是在微分几何，李群，仿射流形等研究中提出的一种复杂的代数体系。

Left-symmetric algebra ( LSA ) is a complex algebra system arising from the study of differential geometry , Lie groups , and affine manifolds .

有限的对称布尔代数都是某个带有一个对合映射的集合X上的集合代数。

All finite symmetry Boolean algebra are set algebra of a certain set X , Which has a doubly mapping .

则P（X）为X的闭理想；（零对称BZ-代数）X为周期BZ-代数的充要条件是X中的每一个理想都是闭理想；

The necessary and sufficient condition of which a zero-symmetric BZ-algebra X is a periodic BZ-algebra is that its every ideal is a closed ideal ;

KdV方程对称李代数的伴随表示及其killing型

The Adjoint Representation for The Symmetry Lie Algebra of KdV Equation and its killing Type

令Sn（F）是元素个数大于3的域F上的n×n对称矩阵代数。

Let Sn ( F ) be the n x n symmetry matrix algebra over the field with | F | > 2 . A partial ordering on matrix algebra is difined .

本文利用群的开拓理论得出了KdV方程对称李代数的伴随表示及其Killing型。

Based on the theory of prolongation , we get the adjoint representation for the Lie algebra of KdV equation and its killing type .

采用GMRES算法求解离散所得的大型非对称稀疏代数方程组。

The GMRES method is used to solve the large non-symmetric sparse algebraic equations .

设F是一个特征不为2的域，Mn（F）和Sn（F）分别记F上的n×n全矩阵代数和对称矩阵代数。

Suppose F is a field of characteristic not 2.Let M_n ( F ) and S_n ( F ) be the n × n full matrix algebra and symmetric matrix algebra over F , respectively .

高维微分-差分模型的Virasoro对称子代数，多线性变量分离解和局域激发模式

Virasoro symmetry subalgebra , multi-linear variable separation solutions and localized excitations of higher-dimensional differential-difference models

在BZ代数中引入元素周期的概念，并讨论了零对称BZ代数元素周期的重要性质。

The notion of periods of elements in BZ algebras is introduced , and its important properties in the frame of zero symmetric BZ algebras are discussed .

本文证明了对称digraph代数上的每一个2-局部导子都是导子，并给出一个例子说明该结论在非对称digraph代数上不成立。

In this paper , we prove that every 2-local derivation from any symmetric digraph algebra into itself is a derivation . Moreover , we give an example to show that the conclusion may not be true if it has not the condition of symmetry .

零对称BZ-代数的充要条件

On the necessary and sufficient conditions of zero-symmetric BZ-algebras

零对称BZ-代数元素周期的性质

Properties of periods of elements in zero-symmetric BZ-algebras

闭理想与周期零对称BZ-代数

Closed Ideals and Periodic Zero - Symmetric BZ-Algebras

零对称BZ-代数

On Zero symmetric BZ algebras