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 共查询到16条相似文献,搜索用时 93 毫秒
1.
关于完满的Lie超代数   总被引:1,自引:0,他引:1  
In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.  相似文献   

2.
The Frattini Subalgebra of Restricted Lie Superalgebras   总被引:6,自引:0,他引:6  
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 + A2 +… +An, then Фp(L) = Фp(A1) +Фp(A2) +…+Фp(An), where each Ai is a p-ideal of L. We then obtain two results: F(L) = Ф(L) = J(L) = L if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.  相似文献   

3.
We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space,  相似文献   

4.
Kang  Yi Fang  Chen  Zhi Qi 《数学学报(英文版)》2021,37(8):1229-1253
Assume that r is a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, p is a finite dimensional complex super vector space with a nondegenerate super-symmetric bilinear form, and ν : r → osp(p) is a homomorphism of Lie superalgebras.In this paper, we give a necessary and sufficient condition for r ⊕ p to be a quadratic Lie superalgebra.Then, we define the cubic Dirac operator D(g, r) on g and give a formula of(D(g, r))~2. Finally, we get the Vogan's conjecture for quadratic Lie superalgebras by D(g, r).  相似文献   

5.
The authors consider a family of finite-dimensional Lie superalgebras of O-type over an algebraically closed field of characteristic p 3. It is proved that the Lie superalgebras of ■-type are simple and the spanning sets are determined. Then the spanning sets are employed to characterize the superderivation algebras of these Lie superalgebras.Finally, the associative forms are discussed and a comparison is made between these Lie superalgebras and other simple Lie superalgebras of Cartan type.  相似文献   

6.
陈良云  孟道骥 《东北数学》2005,21(3):283-293
In the present paper, we give some sufficient conditions for the commu tativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.  相似文献   

7.
We study class of finite-dimensional Cantan-type Lie superalgebras HO(m) over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO(m).  相似文献   

8.
The aim of this paper is to introduce and study Hom-Gel'fand–Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing HomGel'fand–Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel'fand–Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel'fand–Dorfman super-bialgebras.  相似文献   

9.
ON SOLVABLE COMPLETE LIE SUPERALGEBRAS   总被引:1,自引:0,他引:1  
The authors discuss the properties of solvable complete Lie superalgebra, proving that solvable Lie superalgebras of maximal rank are complete.  相似文献   

10.
In this paper,all symmetric super-biderivations of some Lie superalgebras are determined.As an application,commutative post-Lie super algebra structures on these Lie super algebras are also obtained.  相似文献   

11.
佟洁  张永正 《数学学报》2006,49(1):231-240
对于给定的负阶化李超代数K-,本文定义了K-型泛阶化李超代数并证明了它的存在性.进而引出阶化Cartan型李超代数,并且证得阶化Cartan型李超代数 W(m,n),K(m,n,ωA),S(m,n)和H(m,n)分别可以用某种泛阶化李超代数来刻画.  相似文献   

12.
李超代数的一个性质P叫做关于泛包络代数的不变量,如果对于任意李超代数L,H,只要L具有性质P,并且泛包络代数U(L)和U(H)作为结合超代数是同构的,那么H亦具有性质P.通过讨论李超代数关于泛包络代数的不变量证明了:如果L的幂零长度不超过2,那么L和H是同构的.  相似文献   

13.
John R. Faulkner 《代数通讯》2013,41(9):3268-3310
This article classifies simple structurable superalgebras with nontrivial involution over algebraically closed fields of characteristic 0 whose Kantor Lie superalgebra is of classical (i.e., non-Cartan) type. These are either structurable superalgebras of a hermitian superform or two examples constructed from cubic forms. It also makes extensive use of the Grassmann envelope to transfer constructions and results from ordinary algebras to superalgebras.  相似文献   

14.
通过δ-Jordan李超代数T的表示和上同调理论,构造δ-Jordan李超代数T■V.证明了δ-Jordan李超代数的等价交换扩张给出相同的表示.通过δ-Jordan李超代数的表示和其交换扩张得到2-上圈.  相似文献   

15.
王秀玲  刘文德 《数学进展》2007,36(6):710-720
本文应用象空间极小维数的方法研究了Cartan型模李超代数HO的非平凡可迁滤过(HO,R)的不变性.应用滤过的不变性得到模李超代数HO的某些内蕴性质,从而得到此类李超代数在同构意义下的分类.  相似文献   

16.
孙丽萍  刘文德 《数学学报》2021,64(1):167-176
本文将模李代数中环面与环面秩的理论推广到模李超代数中.应用模李超代数的限制包络得到了环面秩的若干重要性质.作为应用,计算了典型李超代数slm|n与限制Cartan型李超代数W(m,n,1),S(m,n,1)的绝对环面秩及S(m,n,1)在W(m,n,1)中的环面秩.  相似文献   

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