李Rinehart代数的子代数若干性质

本文主要把李代数的c-可补、E-代数的性质以及Frattini理论推广到更为广泛的李Rinehart代数,得到它们的若干性质,给出了可解李Rinehart代数的一个必要条件.同时,分别获得判断c-可补李Rinehart代数和E-李Rinehart代数的一个充分必要条件.     

n+1维n-Lei代数的导子代数

本文给出了n 1维n-Lie代数的导子代数的结构，以及导子的具体表示形式．     

Kleene代数的诱导子代数及理想

由于逻辑学研究的需要 ,Kleene代数理论的重要性已越来越明显 .本文主要研究了Kleene代数的子代数及理想的一些性质 ,得到了一些比较好的结果 .     

三元代数的乘子代数

将L.Harris在[1]中关于三元代数的概念一般化，并且提出了相对近似单位元，相对Arens乘积，相对m-对称等概念，最后得到一个同构定理。     

5维Bernstein-Jordan代数的导子代数

Ⅰ．Ｃｏｒｒｅａ和Ｌ．Ａ．Ｐｅｒｅｓｉ对实数域上的５维Ｂｅｒｎｓｔｅｉｎ－Ｊｏｒｄａｎ代数进行了分类．本文在此基础上，确定了这些代数的导子代数     

三维Leibniz代数的分类

Leibniz代数是比Lie代数更广泛的一类代数,它通常不满足反交换性.在这篇文章里我们确定了维数等于3的Leibniz代数的同构类.     

辛三代数的Frattini子代数

本文研究了辛三代数的Frattini子代数和基本辛三代数的问题.利用Frattini子代数和基本辛三代数的性质,得到了辛三代数的非嵌入定理,从而推广了李三系中关于Frattini子系的结果.     

辫子Hopf代数的因子分解

我们获得了辫子双代数和辫子Hopf代数的双重分解, 给出了辫子Hopf代数的积分和半单性与它的因子的积分和半单性之间的关系.     

Centralizers in free Poisson algebras

We prove an analog of the Bergman Centralizer Theorem for free Poisson algebras over an arbitrary field of characteristic 0. Some open problems are formulated.

     

The order of a group of even order

We will give an estimation of the order of a group of even order by the order of the centralizer of an involution using the classification of finite simple groups.

     

Finite groups and the fixed points of coprime automorphisms

Let be a prime, and let be a finite -group acted on by an elementary abelian -group . The following results are proved:

1. If and is nilpotent of class at most for any , then the group is nilpotent of -bounded class.

2. If and is nilpotent of class at most for any , then the derived group is nilpotent of -bounded class.

     

中心化子的刻画

令X为实或复域F上的Banach空间,■为X上的标准算子代数,I是■的单位元.设Φ:■→■是可加映射.本文证明了,如果有正整数m,n,使得Φ满足条件Φ(A~(m+n+1))-A~mΦ(A)A~n∈FI对任意A成立,则存在λ∈F,使得对所有的A∈■,都有Φ(A)=λA.同样的结果对于自伴算子空间上的可加映射也成立.此外,本文还给出了中心素代数上满足条件(m+n)Φ(AB)-mAΦ(B)-nΦ(A)B∈FI的可加映射Φ的完全刻画.     

Centralizers of finite Blaschke products

In this article we consider the set of finite Blaschke productsF of degreen>1. We give sufficient conditions forF to commute only with their own powers among all rational functions of the Riemann sphere, in terms of the derivate around the fixed points.The author was partially supported by CNPq, Brazil.     

Positive laws in fixed points

Let be an elementary abelian group of order at least acting on a finite -group in such a manner that satisfies a positive law of degree for any . It is proved that the entire group satisfies a positive law of degree bounded by a function of and only.

     

Torus actions on symplectic orbi-spaces

Which -dimensional orbi-spaces have effective symplectic - torus actions? As shown by Lerman and Tolman (1997) and Watson (1997), this question reduces to that of characterizing the finite subgroups of centralizers of tori in the real symplectic group . We resolve this question, and generalize our method to a calculation of the centralizers of all tori in .