模糊软李子代数的概念和性质

借助模糊软集的概念,在李代数上定义了模糊软李子代数和模糊软李子代数之间的模糊软同态,对它们的并、交与和的性质进行了研究,证明了:设L是域F上的李代数,若(f,A)和(g,B)是L上的模糊软李子代数,则(f,A)(g,B)和(f,A)∧(g,B)仍然是L上的模糊软李子代数,但(f,A)∪(g,B)不一定是L上的模糊软李子代数;若(f,A)k是L上的一族预模糊软李理想,则∪k∈K(f,A)k和k∈K(f,A)k仍然是L上的预模糊软李理想.证明了模糊软李子代数的同态逆像定理,给出一个反例以说明模糊软李子代数在同态像下不一定是模糊软李子代数.

模糊预李子代数与模糊Novikov子代数

引入了模糊预李子代数、模糊Novikov子代数和模糊邻接李子代数的概念,讨论了几类常见预李代数、Novikov代数的模糊结构,并分别给出了一类特殊的Novikov代数和一类可以诱导出Burgers方程的预李代数构成模糊代数结构的条件.

关于gl(V)的一维李子代数的正规化子塔的高

设V是复数域C上的n维向量空间,gl(V)为V的所有线性变换组成的李代数。gl(V)的李代数L的正规化子定义为N(L)={τ∈gl(V)|[τ,L](?)L}。若L=N(L),就称L是自正规的。归纳定义L的一系列正规化子:N_0(L)=L,N_1(L)=N(L),…,N_(i+1)(L)=N(N_i(L)),得正规化子塔N_0(L)(?)N_1(L)(?)…(?)N_i(L)(?)…。

一般域上无限矩阵李代数的y-型李子代数

本文在无限矩阵李代数ｇｌ_∞（Ｆ）中定义了 ｙ－型李子代数ｇｌ_∞（ｙ）和 ｓｌ_∞（ｙ），刻划了它们的结构．并证明了ｙ－型李子代数 ｇｌ_∞（ｙ）是单李代数．把文［１］中 ｇｌ_∞（Ｃ）的多项式李子代数 ｇｌ_∞（ｐ（ｔ））和ｇｌ_∞（ｐ（ｔ））在ｙ－型李子代数下得到了统一，指出了 ［１］中ｇｌ_∞（ｐ（ｔ））结构刻划的不完善情形，并在本文定理３中得到了正确的刻划。

Loop代数的多项式李子代数

给出了 Ｌｏｏｐ 代数的所有 Ｓｈｉｆｔ 算子，讨论了 Ｌｏｏｐ

无限矩阵李代数的广泛李子代数

在无限矩阵李代数 g1∞(C)中定义了一类广泛的李子代数 ,并在一定条件下刻划了这类子代数的内部结构 。

无限矩阵李代数的多项式李子代数

在无限矩阵李代数中定义了多项式李子代数，研究了这类李代数的主要性质和它的结构，并在一定条件下证明了此类李代数是单李代数。

一类无限矩阵李代数的李子代数

本文在无限矩阵李代数 gl∞ ( C)中定义了一类广泛的李子代数 ,并在一定条件下刻划了这类子代数的内部结构 。

ad_X作用下的模糊李理想和李子代数

将李代数中导子的概念应用到模糊李理想和模糊李子代数中 ,并讨论了它们的一些性质 ,得出了一些有意义的结果 .

Lazard ss Elimination Process for Color Lie Superalgebras *

A pattern of Lazard*ss elimination theorem for color Lie superalgebras is proved.

On braided Lie algebras

Let （C, C） be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category （C, C） is investigated. First, a braided C2-commutative algebra in the category （C, C） is defined and three equations on the braiding in the category （C, C） are proved. Secondly, it is verified that （A, [, ] ） is a left （strict） Jacobi braided Lie algebra if and only if （A, [, ] ） is a braided Lie algebra, where A is an associative algebra in the category （C, C）. Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel＇d modules and the category of Hopf bimodules.

Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp（4,R） Lie Algebra

Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).

Lie algebraic analysis for the beam transport in the spherical electrostatic analyser

This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.

Realization of Vertex Operators of 7-Twisted Affine Lie Algebra ■[θ]

In this paper, we construct a new algebra structure 7-twisted atone Lie algebra sl（3,C）[θ] and study its vertex operator representations.

Lie Algebraic Approach to Energy Transfer for Collinear Collision of Two Anharmonic Diatomic Molecules

An anharmonic oscillator algebra model is used to study the collinear collisions of two diatomic molecules. The transition probability for vibration-vibration energy transfer is presented. For an application of the method, we talk about the collision of N2＋CO, N2＋O2, and N2＋N2. Through long time averaging, the transition probability changes to the function of total energy of the system. Comparing the results with the quantum results, we can see that the dynamical Lie algebraic method is useful for describing the anharmonie diatomic molecular collision.

The Derivation Algebra of the Cartan-type Lie Superalgebra H

In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.

Boundeness of a Class of Maximal Operators on H^p Spaces on Compact Lie Groups

In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.

Studies of Rigid Rotor-Rigid Surface Scattering in Dynamical Lie Algebraic Method

The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule-surface scattering. It can give the time-evolution operators about the low power of and by solving a set of coupled nonlinear differential equations. For considering the contribution of the high power of and , we use the Magnus formula. Thus, with the time-evolution operators we can get the statistical average values of the measurable quantities in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of (rigid rotor) by a flat, rigid surface to illustrate its general procedure. The results demonstrate that the method is useful for describing the statistical dynamics of gas-surface scattering.

On a Result of Pointed Representations of finite Dimensional Simple Lie Algebras

There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite -dimesional simple Lie algebras are all Harish-Chandra modules.

Derivations of Certain Lie Algebras of Upper Triangular Matrices over Commutative Rings

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the derivation algebras of the Lie algebras t and b, respectively.