G2型2-Toroidal李代数的顶点表示

在[4]和[5]中已经研究了sim p ly-laced型T oro idal李代数的顶点表示,[6]文据此给出了Bl型T oro idal李代数顶点表示的构造.受[6]文启发,本文给出了G2型T oro idal李代数的顶点表示的构造,这种构造方式与D(41)的D ynk in图的顶点粘合和一个2上循环有着紧密联系.     

The Derivation Algebra of Lie Algebra H（n，m） of Cartan Type of Characteristic p＝2

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限制李Color代数

讨论了限制李color代数的Frattini理论,获得了限制李color代数的Frattini子代数和Frattini p-子代数的一些结果,给出了可解限制李color代数的Frattini子代数和Frattini p-子代数都是幂零理想的结论.     

项链李代数的性质

研究项链李代数的性质,给出了其中心元的表示形式,证明了项链李代数非半单、非可解,通过构造项链李代数的可解非幂零子代数,证明了当箭图中有长度大于1的循环时,项链李代数非幂零.还给出了没有圈的箭图上项链李代数的分解.     

项链李代数的结构

研究项链李代数的结构,定义了箭图Q的重箭图Q循环上的映射σ,证明了这是一个李运算.引入左右指标数组概念,利用它们把项链李代数N_Q的基分成了5类,并构造了项链李代数的一些有趣的子代数.     

The Decomposition of Lie Powers

Let G be a group, F a field of prime characteristic p and Va finite-dimensional FG-module. Let L(V) denote the free Liealgebra on V regarded as an FG-submodule of the free associativealgebra (or tensor algebra) T(V). For each positive integerr, let L^r (V) and T^r (V) be the rth homogeneous components ofL(V) and T(V), respectively. Here L^r (V) is called the rth Liepower of V. Our main result is that there are submodules B₁,B₂, ... of L(V) such that, for all r, B_r is a direct summandof T^r(V) and, whenever m 0 and k is not divisible by p, themodule is the direct sum of , . Thus every Lie power is a direct sum of Lie powers of p-powerdegree. The approach builds on an analysis of T^r (V) as a bimodulefor G and the Solomon descent algebra. 2000 Mathematics SubjectClassification 17B01 (primary), 20C07, 20C20 (secondary).     

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.     

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.     

逆步李代数g(A)的导子代数

本文对逆步李代数g(A)的导子代数进行了研究.这里A是任意一个n×n阶的复矩阵,而g(A)是和其相关联的逆步李代数.特别地,当A是广义Caftan矩阵时, g(A)则为Kac-Moody代数.在这里,我们得到了g(A)的导子代数的结构.     

Direct Sum Decomposition of L2(Rn 1) into Subspaces Invariant under Fourier Transformation

Denote by the real-linear span of , where Under the concept of left-monogeneity defined through the generalized Cauchy-Riemann operator we obtain the direct sum decomposition of

filiform李代数R_n的triple导子

对filiform李代数R_n的triple导子进行了研究.利用triple导子的定义,通过计算线性变换在一组特殊的基上的作用结果,得到了filiform李代数R_n的triple导子的矩阵形式,并发现其triple导子代数是一个维数为2n-1的可解李代数.     

KdV方程对称李代数的伴随表示及其killing型

本文利用群的开拓理论得出了 Kd V方程对称李代数的伴随表示及其 Killing型 .     

The Lie Algebra of Homeomorphisms of the Circle

We define and study an infinite-dimensional Lie algebrahomeo₊which is shown to be naturally associated to thetopologicalLie grouphomeo₊of all orientation-preserving homeomorphisms of the circle. Roughly, we rely on the universal decorated Teichmüller theory developed before as motivation to provide Fréchet coordinates on the homogeneous space given byhomeo₊modulo the group of real fractional linear transformations, whose corresponding vector fields on the circle we then extend by the usual Lie algebrasl₂of real traceless two-by-two matrices in order to definehomeo₊. Surprisingly,homeo₊turns out to be equal to the algebra of all vector fields on the circle which are “piecewisesl₂” in the obvious sense. It is evidently important to consider the relationship between our new Fréchet coordinates and the usual trigonometric functions on the circle, and we undertake here both natural infinitesimal calculations. We finally apply some further previous work in order to give sufficient conditions on the Fourier coefficients of a certain class of homeomorphisms of the circle which arises naturally in topology and number theory.     

一般扭算子李代数

由扭算子构成的扭算子李代数在李代数理论中占有重要的位置,首先构造了一般形式的扭顶点算子Z~σ(E_(ij),α,β,z),然后给出了一般扭算子李代数g(G,l)[σ],研究了一般扭顶点算子所具有的性质.     

On the Restricted Lie Algebra Structure of the Witt Lie Algebra in Finite Characteristic

The article contains an explicit formula for the restricted Lie algebra structure in the Witt Lie algebra over a field of finite characteristic. Some combinatorial lemmas can be of independent interest.     

A(m,n)型余分裂李超代数

详细讨论了A(m,n)型余分裂李超代数的结构及其李超代数伴随表示,Killing型和李余超代数结构之间的关系.     

Jordan李超代数的分解再论

代数A称为不可分解的,如果A不能分解成理想的直和.满足C(Lo)=C(L)={0}的Jordan李超代数L能够分解成不可分解理想的直和,这种分解在不计理想次序的前提下是唯一的.并证明了完备Jordan李超代数的一些性质.