On the structure of split Leibniz triple systems

We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized.     

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral <Emphasis Type="Italic">su</Emphasis>(2) WZNW Model

A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.      

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified antiSnyder models

In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.     

新型Poisson括号意义下的无穷维Lie代数

本文首先针对ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式，建立一种比较容易验证的新型Ｐｏｉｓｓｏｎ括号和无穷维Ｌｉｅ代数．其次，研究ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式的第一积分与新型Ｐｏｉｓｏｎ括号的关系，得到判定第一积分的充分必要条件．最后，构造ＫｄＶ方程的第一积分．     

Dm型正交代数的极大幂零子代数上保零李括积的映射

令F表示任意域,l_(2m)(F)表示F上D_m型正交李代数的极大幂零子代数.本文的目的是当m≥5时,刻画l_(2m)(F)上的每一个双向保零李括积的映射.利用文献[7]的主要结果和矩阵计算技巧,本文证明了l_(2m)(F)上的一个线性映射φ是双向保零李括积的当且仅当φ能够写成内自同构,图自同构,广义的对角自同构,中心映射,次中心自同构,极端映射和标量乘法的乘积.这推广了文献[7]的主要结果.     

Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

DERIVATION ALGEBRAS OF THE MODULAR LIESUPERALGEBRAS W AND S OF CARTAN-TYPE

1NatationandPreliminariesWeknowthatthederivationalgebrasisaveryusefulsubjectintheresearchoftheLiealgebrasandLiesupealgebras.Inpapersl1]and[2]thederivationalgebrasofmodularLiealgebrasofCartan-typeareinyestigaved.Inpaper[3]thederivationalgebrasofsimpleLiesuperalgebrasoverfieldsofcharacteristiczeroaredeterndned.Inthispaperthederivational-gebrasofmodularLiesuperalgebrasWandSofCartan-typearedeterminedbythecalculatingmethod-LetFbeafieldandcharF=p>3-WesimPlydescribetheLiesuperalgbrasWandSwhic…     

On the invariant translation approximation property for discrete groups

Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.

     

严格循环的算子代数

设X是半自共轭的Banach空间,而A是B(X)的严格循环的交换子代数,考虑算子代数A的一些性质,这些性质与算子代数的自反性有关,而且这些性质为讨论A的自反性提供了理论基础.