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1.
王栓宏 《数学年刊A辑》2000,21(5):547-552
在Yetter-Drinfel'd范畴中,本文研究了ρ-Lie代数的可解理想结构,得到了如果L是一个H-单的ρ-Lie代数而且V?[L,L]ρ是[L,L]ρ的一个ρ-Lie理想满足V[L,L]ρ.那么V是[L,L]ρ的一个可解ρ-Lie子代数.  相似文献   

2.
3-LIE BIALGEBRAS     
3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.  相似文献   

3.
Metric n-Lie algebras have wide applications in mathematics and mathematical physics. In this paper, the authors introduce two methods to construct metric (n+1)-Lie algebras from metric n-Lie algebras for n≥2. For a given m-dimensional metric n-Lie algebra(g, [, ···, ], B_g), via one and two dimensional extensions £=g+IFc and g0= g+IFx~(-1)+IFx~0 of the vector space g and a certain linear function f on g, we construct(m+1)-and (m+2)-dimensional (n+1)-Lie algebras(£, [, ···, ]cf) and(g0, [, ···, ]1), respectively.Furthermore, if the center Z(g) is non-isotropic, then we obtain metric(n + 1)-Lie algebras(L, [, ···, ]cf, B) and(g0, [, ···, ]1, B) which satisfy B|g×g = Bg. Following this approach the extensions of all(n + 2)-dimensional metric n-Lie algebras are discussed.  相似文献   

4.
文章主要研究n-Lie 代数的扩张问题. 首先利用n-Lie 代数的模作n-Lie 代数的Tθ- 扩张与Tθ*-扩张. 再利用模度量3-Lie 代数,做3-Lie 代数的双扩张. 文章最后利用4- 指标阵构造了m 维3-Lie代数的双扩张.  相似文献   

5.
Associative multiplications of cubic matrices are provided. The N3-dimensional 3-Lie algebras are realized by cubic matrices, and structures of the 3-Lie algebras are studied.  相似文献   

6.
The purpose is to introduce the notions of 3-Bihom-ρ-Lie algebras and 3-preBihom-ρ-Lie algebras. The authors describe their constructions and express the related lemmas and theorems. Also, they define the 3-Bihom-ρ-Leibniz algebras and show that a3-Bihom-ρ-Lie algebra is a 3-Bihom-ρ-Leibniz algebra with the ρ-Bihom-skew symmetry property. Moreover, a combination of a 3-Bihom-ρ-Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom-ρ-Lie algebra structure.  相似文献   

7.
三角代数上的Jordan零点ξ-Lie可导映射   总被引:1,自引:1,他引:0  
给出了三角代数上Jordan零点ξ-Lie可导映射的结构.作为应用,得到了套代数上Jordan零点ξ-Lie可导映射的具体形式.  相似文献   

8.
王栓宏 《中国科学A辑》1999,29(12):1065-1070
在Yetter-Drinfeld范畴中 ,研究了导出ρ-Lie代数的中心不动集.  相似文献   

9.
设A是维数大于1的因子von Neumann代数且ξ≠1.本文给出了A上非线性*ξ-Lie可导映射的结构·作为应用,得到了B(H)上非线性*ξ-Lie可导映射的具体形式.  相似文献   

10.
主要研究3-Lie代数的子代数及次理想的结构.证明了由次理想生成的子代数不一定是次理想.给出了由次理想生成的子代数是次理想的充要条件.最后研究了次理想和子代数的G_n-对之间的关系.  相似文献   

11.
本文研究具有平凡中心的有限维的n-Lie代数的分解及唯一性问题(定理2.2),而且证明了具有非平凡中心的n-Lie代数结论不成立.同时研究了n-Lie代数的导子代数及内导子代数的分解问题(定理2.1).  相似文献   

12.
In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.  相似文献   

13.
n+1维n-Lei代数的导子代数   总被引:15,自引:1,他引:14  
本文给出了n 1维n-Lie代数的导子代数的结构,以及导子的具体表示形式.  相似文献   

14.
基本n-Lie代数   总被引:2,自引:0,他引:2  
白瑞蒲  张艳艳 《东北数学》2007,23(4):321-334
In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras and E-algebras.  相似文献   

15.
两类幂零的n-Lie代数   总被引:4,自引:1,他引:3  
白瑞蒲  孟道骥 《数学学报》2005,48(5):909-918
本文提出并构造了两类幂零的n-Lie代数:特征幂零的n-Lie代数与最大秩的幂零的n-Lie代数.证明了n-Lie代数是特征幂零的n-Lie代数的充分必要条件,以及最大秩的幂零的n-Lie代数的结构特征.  相似文献   

16.
白瑞蒲  孟道骥 《数学进展》2006,35(6):739-746
本文主要研究了强半单的n-李代数的表示,证明了强半单的n-李代数的表示(V,ρ)可转化为一个约化李代数Lρ(V)的表示,并证明了不变线性形等其它相关性质.  相似文献   

17.
The Frattini Subalgebra of n-Lie Algebras   总被引:3,自引:0,他引:3  
In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.  相似文献   

18.
该文证明了n - 李代数的Jordan-Holder 定理, 并对n - 李代数的饱和态像进行系统的研究.  相似文献   

19.
对φ-free n-Lie代数的判别条件作了探讨,得到了由n-Lie代数的幂零根基表示的充要条件,并对φ-free n-Lie代数的性质作了研究.  相似文献   

20.
利用结合代数与n-李代数的张量积构造了一类无限维特征单的n-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数是特征单李代数.  相似文献   

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