交换半环上三角矩阵代数的自同构

证明了如果尺是含有恒等元的交换半环，那么R上的n阶上三角矩阵代数的自同构都是内自同构．     

主理想整环上对称矩阵的非结合代数自同构

本文研究了一类非结合代数的自同构.利用分式化方法,得到主理想整环上对称矩阵构成的非结合代数的所有自同构形式,并刻画了相应的Jordan自同构.     

C~*标准代数中效应的序列同构

主要借助于C~*标准算子代数中的有限秩算子对一般的效应元进行刻画.证明了C~*标准算子代数A的效应代数E(A)上的每个序列自同构和自同构ψ都具有形式ψ(A)=UAU~*,其中A∈E(A),U为酉算子或反酉算子.     

一类推广的Virasoro-like李代数

构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.     

形式三角矩阵环的导子和自同构

本文研究了形式上三角矩阵环Tri(A,M,B)的导子和自同构,利用与单位元相乘的方法,获得了形式上三角矩阵环Tri(A,M,B)的导子和自同构的结构形式.     

可换环上上三角矩阵代数的若当自同构分解(英文)

设R是含单位元1和可逆元2的可换环,Tn+1(R)表示R上(n+1)×(n+1)级上三角矩阵全体所形成的矩阵代数.本文证明了T(R)的每一个若当自同构都可唯一的分解为图自同构,内自同构和对角自同构的乘积.     

多项式代数的一类新的试验多项式 *

域上多项式代数K[ X ]中的一个多项式p称为试验多项式 ,如果代数K[ X]的每个固定p的自同态必为自同构 .给出了一类新的试验多项式 ,可识别多项式代数的非线性自同构 .对于域K的特征为奇素数的情形 ,构作了可识别非半单自同构的试验多项式 .     

Cartan型李代数的自同构群

本文证明了素特征域 Ｆ上广义 Ｃａｒｔａｎ型李代数的自同构群都是 ＡｕｔＷ（ｍ,ｎ）的子群．文中对于除幂代数相应的可容许自同构给出了刻划,从而对广义 Ｃａｒｔａｎ型李代数的自同构给出了刻划     

形式向量场的一般Lie超代数与特殊Lie超代数

证明了形式向量场的一般Lie超代数W与特殊Lie超代数S的自然滤过是不变的.进而证明了W与S的自同构群同构于它们的底代数U的可许自同构群,于是W与S的自同构都是由U的连续自同构所诱导的.     

一类W-代数的导子和自同构

讨论了一类W-代数,这类李代数包含无中心的广义Virasoro子代数.本文确定了这类李代数的导子和自同构.     

Automorphism groups of pointed Hopf algebras

The group of Hopf algebra automorphisms for a finite-dimensional semisimple cosemisimple Hopf algebra over a field k was considered by Radford and Waterhouse. In this paper, the groups of Hopf algebra automorphisms for two classes of pointed Hopf algebras are determined. Note that the Hopf algebras we consider are not semisimple Hopf algebras.      

Structure of weak automorphism groups of mono-unary algebras

A weak automorphism of an algebra on A with the set T of term operations is a permutation of of A such that . In this note we describe the groups of weak automorphisms of mono-unary algebras. Some examples of such algebras without weak automorphisms are given. Received January 31, 1996; accepted in final form March 16, 1999.     

Automorphisms of Tensor Completions of Algebras

In the classical representation of different groups, frequent use is made of a linear automorphism group of various algebras. Since the linear automorphism group is only part of a full automorphism group, such an approach might seem to be too restrictive. In this connection, we point out a natural, wide class of algebras whose automorphisms are standard and are reducible to linear. Thus, for algebras in this class, studying the full automorphism group reduces to treating the linear, a traditional approach in the class of such algebras being quite general.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 368–382, May–June, 2005.     

Ternary mappings of triangular algebras

Aequationes mathematicae - We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of...     

GROUPS OF AUTOMORPHISMS OF CHEVALLEY ALGEBRAS

In the paper we present an extension of Segal theorem on Lie algebra automorphisms of upper triangular nilpotent matrices to the whole class of nilpotent subalgebras generated by positive parts of indecomposable Chevalley algebras.     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.