从那时开始，人们发现量子群在很多领域都有着深刻的应用，范围遍及理论物理、辛几何、扭结理论与约化代数群的模表示理论等。
Since then they have found numerous and deep applications in areas ranging from theoretical physics, symplectic geometry, knot theory, and modular representations of reductive algebraic groups.
代数群的连通正规闭子群与李代数的理想之间有很特殊的关系。
There are particular relations between the closed connected normal subgroups of algebraic groups and the ideals of Lie Algebras.
代数群的连通正规闭子群与李代数的理想之间有很特殊的关系。
Some algebraic groups are discussed by looking into the lattice of their closed connected normal subgroups.
基本思想是首先利用圆盘状单裂纹之解以及局部坐标展开法将裂纹群问题化为求解一组线代数方程。
The basic idea is to use the single crack solution and the expansions of the local coordinates to reduce the complicated problem into a set of linear algebraic equations.
本文通过对合交换半群概念的引入，对MV-代数建立了几组等价公理系，对原有的公理系进行了较好的简化。
In this paper, we introduce the notion of involution commutative semi-group, and give some equivalence axioms of MV - algebras.
基于旋转群代数，以航天器姿态控制研究为背景，提出了四元数的核心矩阵的概念。
A concept of kernel matrix of quaternion is proposed, which is based on rotation group algebra and with spacecraft attitude control as its background.
通过抽象代数知识，求出所有正多面体的旋转群。
Using the knowledge of abstract algebra, the rotation groups of the regular polyhedron are determined.
本文试图用群的思想考察初等代数中的部分内容。
In this paper, we attempt to inspect partially the content of school algebra with the idea of group.
主要考虑非线性波方程组的一些简单对称及其构成的李代数，并利用所得对称给出该方程组的一些单参数变换群。
In this paper, the symmetries and Lie algebra of a coupled nonlinear wave equation were discussed. One-parameter transformation groups of this equation were obtained by using the symmetries.
十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。
In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.
针对代数法和卡诺图法难以化简规模很大的逻辑函数问题，提出使用蚁群算法处理大规模逻辑函数化简。
As algebra way and map way can not simplify the given large scale logical function, a new way using Ant Colony Algorithm to simplify large scale logical function is put forward.
运用基础代数中有关自同构、左平移、正规子群等理论，对群G的全形进行了简单的探讨，证明了几个有关的结论。
By using the theories in basic algebra about automorphism, left translation and normal subgroup, in the holomorph of G is discussed briefly, and several related conclusions are obtained.
半群的研究在代数学的理论研究中占有很重要的地位。 其中格林关系在半群理论的研究中有着重要的意义。
The research of semigroup plays an important role in the research of the theory of algebra, and the Green's equivalences are especially significant in the study of semigroups.
半群平移壳理论是半群代数理论的一个重要部分，在半群的理想扩张理论中占有重要地位。
The theory of translational hull of semigroups is an important branch of the algebra theory and plays a basic role in the theory of ideal extensions of semigroups.
利用代数思想及方法证明直觉模糊群的诱导商集也是直觉模糊群。
By using algebraic methods, it was proved that the induced quotient set determined by an intuitionistic fussy group was still an intuitionistic fussy group.
讨论了李超代数上的左超对称结构与其上的1维上同调群的关系。
It discusses the relationship between left-supersymmetric structures on Lie superalgebra and its 1 th cohomology group.
首先根据有限交换群上对称双特征标的概念，给出着色李超代数的定义，并介绍关于着色李超代数的一些基本概念与基础知识。
First, we give the definition of Lie color superalgebras using the symmetric bicharacter on a finite commutative group, and also we introduce some fundamental notions about Lie color superalgebras.
进而，从对称的观点说明婚姻形式从简单到复杂的演化过程，代数上对应于对称群阶数的增加，几何上则对应于对称性的加强。
Furthermore, it illustrates when the form of marriage changes from simplicity to complexity, the group has better symmetry on geometry, the order of the group is h...
进而，从对称的观点说明婚姻形式从简单到复杂的演化过程，代数上对应于对称群阶数的增加，几何上则对应于对称性的加强。
Furthermore, it illustrates when the form of marriage changes from simplicity to complexity, the group has better symmetry on geometry, the order of the group is h...
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