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 共查询到19条相似文献,搜索用时 62 毫秒
1.
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   

2.
限制李超代数的诱导模   总被引:2,自引:0,他引:2  
刘文德 《东北数学》2005,21(1):54-60
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.  相似文献   

3.
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   

4.
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   

5.
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   

6.
袁鹤 《东北数学》2008,24(5):399-408
In the paper, we give some results about a linear combination of superderivations on prime superalgebras and generalize a result of Niu Feng-wen.  相似文献   

7.
In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.  相似文献   

8.
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   

9.
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   

10.
Abstract In this paper, the super t~-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super б-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super б-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established. Keywords Super б-operator, dendriform superalgebra, pre-Jordan superalgebra  相似文献   

11.
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   

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15.
In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland's theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.  相似文献   

16.
Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L; up to equivalence of extensions. Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms. Finally, we describe the multipliers, covers, and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.  相似文献   

17.
李超三系的分解唯一性   总被引:1,自引:0,他引:1       下载免费PDF全文
该文首先研究了李超三系的中心、导子超代数和内导子超代数的分解问题, 给出了具有平凡中心的李超三系的分解唯一性定理, 同时讨论了李超三系的自同构的扩张.  相似文献   

18.
In the previous part of this study we considered universal central extensions of Lie conformal algebras and conditions for existence of such extensions. The aim of this paper is some refinement of previous results and extension of these results to Lie conformal superalgebras.  相似文献   

19.
Dong Liu 《代数通讯》2013,41(6):1814-1823
The universal central extensions and their extension kernels of the smatrix Lie superalgebra 𝔰𝔩(m, n, 𝒜), the Steinberg Lie superalgebra 𝔰𝔩(m, n, 𝒜) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with Mikhalev and Pinchuk, 2000 Mikhalev , A. V. , Pinchuk , I. A. ( 2000 ). Universal central extension of the matrix Lie superalgebras sl(m, n, A) . Contemp. Math. 264 : 111126 . [Google Scholar]) using the first Hochschild homology and the first cyclic homology group.  相似文献   

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