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- Let A be a symmetrizable generalized Cartan matrix, g(A) thecorresponding Kac-Moody algebra, then a subalgebra h of g(A) is a split Cartan subalgebra if and only if there is a regular locally finite element x such that h=g 0(adx). 设A为一可对称化广义Cartan矩阵 ;g(A)为对应的Kac_Moody代数 ;则 g(A)的子代数h为可裂Cartan子代数的充分必要条件为存在正则局部有限元x ;使得h =g0 (adx) .
- All finite-dimensional path lie algebras are solvable and their Cartan subalgebras of them are obtained. 给出了有限维路李代数均可解的结论和所有的卡当子代数；
- The root space decompositions of them relative to specific Cartan subalgebras are given. 并给出了其相对于一个特定的卡当子代数的根子空间的分解；
- cartan subalgebra 嘉当子代数
- IS SUBALGEBRA GENERATED BY NILPOTENT ELEMENTS NILPOTENT_? 幂零元生成的子代数是幂零吗?
- Conclusion Every fuzzy subalgebra of a fuzzy P-semisimple BCI-alegbras is also a fuzzy P-semisimple BCI-algebras. 结论说明任一模糊P-半单BCI代数的模糊子代数，也是模糊P-半单BCI-代数。
- In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings. 摘要本文研究了含幺可换环上一般线性李代数的子代数结构。
- Also we proved that any proper subalgebra of a standardKac-Moody algebra g(A) is standard, where A1 is any principle submatrix of A (see Theorem 2.6). 证明了典范Kac-Moody代数g(A)的任一真子代数g(A_1)也是典范的，此处A_1是A的任一主子阵(定理2.;6)。
- It is proved that the Frattini subalgebra of a complete Lie algebra with abelian nilpotent radical is the zero subalgebra. 证明了特征零代数闭域上的具有交换幂零根基的完备Lie代数的Fratini子代数为零。
- Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra. 利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。
- Cartan domain to Hua domain II. 嘉当域到华罗庚域2。
- With the aborative description of geometry and analytics,applying Cartan Method,gets the Euler equation of weakly harmonic maps from high dimension Riemann manifold to homogeneous space. 借助于几何上与分析上的精细刻画;利用卡坦方法;得到高维Riemann流形到齐次空间弱调和映射体现的具体Euler方程形式.
- The basic properties of matrix subalgebra were investiaged, the matrix subalgebra was generated by a single matrix, all maximal ideals were classified, the necessary and sufficient conditions for the subalgebra to be semisimple algebra were given. 摘要研究了由一个矩阵生成的拒阵子代数的基本性质，给出了其极大理想的完全分类及这类子代数是半单代数的充要条件。
- Firstly, we prove three equivalent conditions for a solvable n-Lie algebra. Subsequently, mimicking the Borel subalgebra theory of Lie algebras, we give the definition of a Borel n-subalgebra of an n-Lie algebra, and prove two propositions about it. 第三节，证明了可解n-李代数的三个等价条件，并仿照李代数理论中的Borel子代数的定义，给出了Borel n-子代数的定义及相关性质。
- The Cartan Subring of Kac-Moody Lie Ring Kac-Moody Lie环的Cartan子环
- 2) If g is an irresolvable Cartan solvable Lie algebra, then of with the Borel subalgebra of the nine typical simple Lie algebra is isomorphism. ( ii)若 g是一个不可分解的 Cartan可解李代数 ;则 g与 9种典型单李代数之一的 Borel子代数同构 .
- THE ALGEBRA IN WHICH EVERY SUBSPACE IS SUBALGEBRA 每一个子空间都是子代数的代数
- The Subalgebra Chains of s. d. g IBMs. d
- strongly singular maximal abelian subalgebra 强奇异极大交换子代数
- direct product of Fuzzy subalgebra Fuzzy子代数的直积
