算子理论，算子代数及其应用。
元微分算子代数的导子李代数结构。
Lie algebras of derivations of n-differential operator algebra.
ACUN理论是异或算子代数性质的刻画。
The algebraic properties of the operator exclusive-or are characterized by the ACUN theory.
本文研究了含幺可换环上一般线性李代数的子代数结构。
In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings.
泛函分析和算子代数；量子化方法和路径积分；变分技术。
Functional Analysis and Operator Algebras; Quantization Methods and Path Integration; Variational Techniques.
应用这些新方法和子代数的性质可以深入研究概念的数学本质。
Applying these new ways and the algebra structure of sub algebra, we can study the mathematics essence of the concepts thoroughly.
本文讨论了复(实)数域上的二维李三系的分类及其对应的导子代数的性质。
In this paper, We study the classification and the properties of their derivation algebras of 2-dimensional Lie triple systems over the complex (real) number field.
并通过算子代数的分解以及对称理想的结构给出各类退化算子代数的一般形式。
And give general forms of every class of degenerate operator algebras by the representations of this algebra and constructions of symmetric ideals.
结果得到了拓扑bci代数的拓扑子代数、拓扑理想和拓扑同态的一些相关性质。
ResultsSome related properties of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras are obtained.
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。
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.
讨论了半单广义顶点代数（相应地半单广义顶点算子代数）的若干性质，例如：这些代数的分解；
In this paper, some properties of semisimple generalized vertex algebras (resp. semisimple generalized vertex operator algebras), for example the decompositions of these algebras;
交换环上矩阵代数的可解子代数和幂零子代数的自同构分解问题是一类重要的具有理论意义的研究课题。
It is theoretically important to solve the problems of decomposition of automorphisms of solvable subalgebra and nilpotent subalgebra of matrix algebra over commutative rings.
目的为研究拓扑bci代数的拓扑子代数、拓扑理想和拓扑同态的概念。试图在代数结构中嵌入拓扑结构。
AimTo study the notions of topological subalgebras, topological ideals and topological homomorphisms in topological BCI-algebras.
接着对矩阵代数m_3 (C)的子代数上的2 -上循环进行了等价刻画，得到了其上的双线性映射是2 -上循环的充要条件。
Subsequently, we character and study the 2-cocycles on a subalgebra of the algebra M3 (c) and obtain the necessary and sufficient conditions that a bilinear mapping is a 2-cocycle on this algebra.
接着对矩阵代数m_3 (C)的子代数上的2 -上循环进行了等价刻画，得到了其上的双线性映射是2 -上循环的充要条件。
Subsequently, we character and study the 2-cocycles on a subalgebra of the algebra M3 (c) and obtain the necessary and sufficient conditions that a bilinear mapping is a 2-cocycle on this algebra.
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