一类Weyl型单李超代数

本文研究了单李超代数的构造理论．借助于张量积方法，定义了一类Weyl型结合超代数和一类Weyl型李超代数，并且证明了这类Weyl型结合超代数和Weyl型李超代数是单的充分必要条件．     

Witt型单李超代数

设F是特征p〉2的域,A是F上结合的超交换的代数,D是域为F上A的超交换的导子.设A×D=A[D]为Witt型李超代数.从环论的角度得到了Witt型李超代数为单代数的充分必要条件.     

一类广义W型李超代数

构造了一类有限维广义Caxtan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

一类广义W型李超代数

构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

函数恒等式理论在泊松超代数上的应用(英文)

泊松超代数既是结合超代数又是李超代数.本文利用结合超代数上的函数恒等式理论研究泊松超代数上的映射,将李超代数上的一类映射转化为结合超代数上的映射.     

Hom-李超代数的结构

类比于单李超代数的结构性质,证明了单Hom-李超代数没有任何非平凡的左(右)理想、理想.通过给出保积Hom-李超代数的若干性质,建立了保积Hom-李超代数与李超代数之间的关系.特别地,证明了正则Hom-李超代数是可解(幂零)的充要条件是其容许李超代数是可解(幂零)的,并给出了正则Hom-李超代数是单的必要条件为其容许李超代数是单的.     

有限维模李超代数(-W)

本文构造了有限维模李超代数(-W).利用已有的模李超代数W(m,n,t_),证明了(-W)是单李超代数,获得了(-W)是限制李超代数的一个充分必要条件,进而证明了-W没有非退化结合型.     

Weyl型单代数

对于任意特征的域F上具有单位元的交换结合代数A和它的交换导子的子空间D的多项式代数F［Ｄ］,在张量空间A［Ｄ］=AÄF［Ｄ］中定义了Weyl型结合代数和Lie代数.证明了A［Ｄ］作为Lie代数(模去中心)或结合代数是单的充要条件是A为D-单的并且A［Ｄ］在A上的作用是忠实的.[KG*2]由此可构造出许多单代数.     

量子仿射李超代数Uq(osp(2n+1|2m)(1))的Serre关系

osp(2n+1|2m)⁽⁽¹⁾)是一类非常重要的仿射李代数.其结构不仅含有Serre关系,而且还有高阶Serre关系.本文给出了量子仿射李超代数U_q(osp(2n+1|2m)((1))是一类非常重要的仿射李代数.其结构不仅含有Serre关系,而且还有高阶Serre关系.本文给出了量子仿射李超代数U_q(osp(2n+1|2m)⁽⁽¹⁾))所有Serre关系的详细表达式,对研究该李超代数和量子超代数的表示有着积极的作用.     

Cartan型模李超代数H(0,n)

讨论了素特征域上有限维Cartan型李超代数H(0,n)的单性、限制性和结合型.     

Quadratic Lie Superalgebras Generalized by Balinsky–Novikov Superalgebras

Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.     

关于完满的Lie超代数

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.     

Lie superderivations of superalgebras

The aim of this paper is to investigate Lie superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we obtain a definitive result on Lie superderivations of prime superalgebras.     

四维线状李超代数具有权1的Rota-Baxter算子

根据低维线状李超代数的分类定理,通过计算刻画了复数域C上的四维线状李超代数具有权1的Rota-Baxter算子.     

A class of generalized odd Hamiltonian Lie superalgebras

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）.     

泛阶化李超代数

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．     

EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS

In recent years the Lie superalgebras have become a 8ubject of intere8t in both mathematicsand physic8[']--[41. We know that the embedding theorems of Z-graded Lie superalgebras andfiltered Lie superalgebras play an important role in the investigation of Lie superalgebras. Theembedding theorem of Z-greded Lie superalgebras is already proved in paper [5l. In this paperthe homomorphic realization Of Lie superalgebras is given and proved by tlle method of tlieReff6]. Using the result of honro…     

Some properties of isoclinism in Lie superalgebras

Abstract

Isoclinism of Lie superalgebras has been defined and studied currently. In this article, it is shown that for finite dimensional Lie superalgebras of same dimension, the notation of isoclinism and isomorphism are equivalent. Furthermore, we show that covers of finite dimensional Lie superalgebras are isomorphic using isoclinism concept.     

阶化 Cartan 型李超代数的结合型

本文确定了具有非退化结合型的Ｃａｒｔａｎ型李超代数。     

ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.