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- semisimple subalgebra 半单子代数
- 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。
- IS SUBALGEBRA GENERATED BY NILPOTENT ELEMENTS NILPOTENT_? 幂零元生成的子代数是幂零吗?
- The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces. 然而课程还将简单介绍了基本的黎曼几何和复流形的知识,并会详细讨论半单李群和对称空间的理论。
- A criterion theorem of having no finite coverings for a finitely generated module M over a semisimple ring R is given. 对半单环上有限生成左模给出一个无有限覆盖的判定定理。
- 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。
- On these grounds, the sensitivity of semisimple multiple eigenvalues of generalized eigenvalue problems is defined, and the sensitive elements of matrix pairs can be determined. 以所得结论为基础,定义了广义特征值问题半单重特征值的灵敏度,给出了确定矩阵对中敏感元素的方法。
- 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)。
- In particular, we prove that there are only finitely many equivalence classes for twisted conjugate actions for semisimple Lie groups. 特别地,我们证明了连通半单李群的扭共轭作用只有有限多个等价类。
- 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。
- This paper proves that any dipolarization in a real or complex semisimple Lie algebra is symmetric. Thus a complete answer to the open problem in reference[2] is gaven. 本文证明半单李代数上的任何双极化都是对称的,从而解决了金行壮二于1993年提出的一个待解的问题.;并给出了有关结果的一些应用
- Abstract: This paper proves that any dipolarization in a real or complex semisimple Lie algebra is symmetric. Thus a complete answer to the open problem in reference[2] is gaven. 文摘:本文证明半单李代数上的任何双极化都是对称的,从而解决了金行壮二于1993年提出的一个待解的问题.;并给出了有关结果的一些应用
- 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。
- 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) .
- The concepts of atom and branch are introduced in the BCH algebra, a series of equivalence conditions about judging atom of the BCH algebra are given, It is proved that the set which all atoms of a BCH algebra are made up is a p semisimple BCI algebra. 在 BCH-代数中引入了原子与分支的概念 ;给出了一个元素为 BCH-代数原子的一系列等价条件 ;证明了一个 BCH-代数的所有原子做成的集合是一个 p-半单 BCI-代数 .
- 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。
- After introducing some preliminaries and notations,the paper investigates semisimple Malcev algebras,giving some equivalent definitions and properties of semisimple Malcev algebras. 在列举了一些马力茨夫代数的基本知识之后;主要讨论了半单马力茨夫代数.;给出了半单马力茨夫代数的几个等价定义和性质
- The concept of FCGP-regular rings and FCGP-IF rings are given.The relations among regular rings, FCGP-regular rings, IF rings and FCGP-IF rings are proved.Finally, it elaborates semisimple rings. 其次,引入FCGP-正则环和FCGP-IF环的概念,证明了正则环、FCGP-正则环和IF环、FCGP-IF环之间的关系,并给出半单环的刻划。
- In particular,a modem approach to the description of automorphisms and gradings of semisimple Lie algebras is given.A special chapter is devoted to models of the exceptional Lie algebras. 该丛书是科学出版社组织学术界多位知名院士、专家精心筛选出来的一批基础理论类数学著作,读者对象面向数学系高年级本科生、研究生及从事数学专业理论研究的科研工作者。