一类新的对称自对偶李代数

本文刻划了一类幂零根基为二步幂零李代数的新的非可解对称自对偶李代数.当其Levi因子同构于sl(2,C)时,用半单李代数的表示理论具体构造了它们.最后,给出了2中对称自对偶李代数是CS李代数的一个判别准则.     

某些完备李代数的结构

本文讨论了完备李代数的同构问题，并对幂零根基为一些Ｈｅｉｓｅｎｂｅｒｇ代数及交换李代数之直和的可解和一般完备李代数的结构进行了讨论．     

具有交换幂零根基的完备李代数的自同构群

给出了复数域上具有交换幂零根基的完备李代数的自同构群．     

关于项链李代数的结构

Le Bruyn和V．Ginzbrug最近引入了项链李代数。它是定义在箭图上的一种无限堆李代数，在非交换几何研究中起了重要作用。本研究项链李代数结构，证明了当箭图中有长度大于1的循环时，其项链李代数不是幂零李代数，我们还给出了没有圈的箭图上项链李代数的分解。     

非零元素ad-幂零或自中心的李代数

研究每一非零元素或 ad 幂零或自中心的李代数 ,得到不可解的这样李代数的秩为 1     

低维幂零李代数的Yang-Baxter算子

在特征零的代数闭域F上,利用3维和4维幂零李代数的分类,通过计算刻画了3维和4维幂零李代数的Yang-Baxter算子.     

相应于一类对称自对偶李代数的顶点代数结构

设gsp是给定的对称自对偶李代数,给出了相应于gsp的一个顶点代数结构.     

一类带有非退化不变对称双线性函数的幂零李代数

本文证明了一类带有非退化不变对称双线性函数、幂零指数为Ｎ的李代数 满足：定理１．（ｉ）ｃ（ｇ）＝ｇ~Ｎ; （ｉｉ）ｄｉｍｃ（ｇ）＝ｌ．ｌ是ｇ的生成元个数．定理３给出了这类李代数结构的充分且必要条件．     

对称自对偶李代数的一些性质

给出了一类带有非退化对称不变双线性型及对称自对偶李代数的分解唯一性的一个充分条件,并讨论此类李代数的特殊性质.     

小特征的有限维Cartan型李代数的滤过

用Ｌ表示Ｃａｒｔａｎ型李代数Ｗ（ｎ，ｍ），Ｓ（ｎ，ｍ）或Ｈ（ｎ，ｍ〕．本文证明了当基域Ｆ的特征数ｐ＝２与３时Ｌ的自然滤过是不变的．从而得到了当ｐ＝２与３时，Ｌ的每个自同构都是由与之相应的除幂代数的自同构所诱导的．     

A-扩张Lie Rinehart代数

The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.     

Depth Generated Simple Lie Algebras

A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra . This determines a depth functor from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows that the Lie algebras corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras are simple for all i ∈ ω. In particular, the (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras. Presented by Don Passman.     

一类模李代数的导子代数(英文)

本文通过构造一类模线状李代数,求出了它的导子代数,并且证明这个导子代数是可解但不完备的模李代数.这将有利于研究一般模线状李代数的结构.     

Derivation Algebra of Quasi Rn-filiform Lie Algebra

In this paper we explicitly determine the derivation algebra of a quasi Rn-filiform Lie algebra and prove that a quasi Pn-filiform Lie algebra is a completable nilpotent Lie algebra.     

关于局部顶点李代数的一些注记

本文研究局部顶点李代数与顶点代数之间的关系.利用由局部顶点李代数构造顶点代数的方法,定义局部顶点李代数之间的同态,证明了同态可以唯一诱导出由局部顶点李代数构造所得到的顶点代数之间的同态.     

Novikov algebras and Novikov structures on Lie algebras

We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any free three-step nilpotent Lie algebra admits a Novikov structure. We study the existence question also for Lie algebras of triangular matrices. Finally we show that there are families of Lie algebras of arbitrary high solvability class which admit Novikov structures.     

Derivation Algebra of Quasi $R_n$-Filiform Lie Algebra

In this paper we explicitly determine the derivation algebra of a quasi $R_n$-filiform Lie algebra and prove that a quasi $R_n$-filiform Lie algebra is a completable nilpotent Lie algebra.     

Constructing affine Lie algebras

The ?-grading determined by a long simple root of a rank n+1 a?ne Lie algebra over ? arises from a representation of a rank n semi-simple complex Lie algebra. Analysis of the relationship between the grading and the representation yields constructions that generalize the minuscule and adjoint algorithms as well as Kac’s construction of nontwisted a?ne Lie algebras.     

由特殊箭图诱导的项链李子代数

无限维项链李代数是新的一类无限维李代数,本文重点讨论了由特殊箭图诱导的项链李子代数,并证明了其中一些李子代数是半单李代数.