三角矩阵代数的自同构

本文研究了三角代数的自同构.利用三角代数的基本概念及自同构定义,得到三角代数的自同构形式,并刻画了其内自同构的具体形式.     

自反算子代数的环自同构

设A是Banach空间X上的自反算子代数,并且A的不变子空间格Lat A满足0+≠0和X_≠X,αA→A是环自同构.如果X是实空间,并且dim X±＞1,则存在X上的线性有界可逆算子A,使得α(T)=ATA-1,T∈A;如果X是复空间,并且dim X±=∞,则α(T)=ATA-1,T∈A.其中AX→X是线性、或者共轭线性有界可逆算子.     

自反算子代数的环自同构

设Ａ是Ｂａｎａｃｈ空间Ｘ上的自反算子代数，并且Ａ的不变子空间格ＬａｔＡ满足 ０＋≠０和Ｘ_≠Ｘ，ａ：Ａ→Ａ是环自同构．如果Ｘ是实空间，并且ｄｉｍ　Ｘ　＞１；则存在Ｘ上的线性有界可逆算子Ａ，使得ａ（Ｔ）＝ＡＴＡ～（－１）；Ｔ∈Ａ：如果Ｘ是复空间，并且ｄｉｍ Ｘ　＝∞，则ａ（Ｔ）＝ＡＴＡ～（－１），Ｔ∈Ａ．其中Ａ：Ｘ→Ｘ是线性、或者共轭线性有界可逆算子．     

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.     

AUTOMORPHISMS OF EXCEPTIONAL SIMPLE LIE ALGEBRAS

The scheme describing automorphisms of exceptional simple Lie algebras possessing geometrical realization over an algebraically closed field of characteristic p < 7 is proposed. In particular, automorphisms of Melikyan algebras g(m ₁, m ₂) (p = 5) and Skryabin algebras Y(m ₁, m ₂, m ₃) (p = 3) are found.     

无限秩仿射李代数的cartan子代数的共轭性

本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性.     

无限秩仿射李代数的Cartan子代数的共轭性

本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性.     

CSL代数中的有限秩算子 Ⅲ

In terms of the exactly nonzero partition,the reducible projection-system and correlation matrices, two characterizations for a rank three operator in a CSL algebra can be completely decomposed are given.     

QUOTIENTS OF 2-SUMMING ALGEBRAS

Abstract

A result of A.M. Mantero and A. Tonge is strengthened by giving an example of a commutative operator algebra which is semisimple but which is not the quotient algebra of a 2-summing Banach algebra by a closed ideal.     

ON K 2 OF DIVISION ALGEBRAS

ABSTRACT

In this paper, it is proved that if F is a global field, then for any integer n > 3, there is an extension field E over F of degree n such that K ₂ E is not generated by the Steinberg symbols {a, b} with a ∈ F*, b, ∈ E*. If however, F is a number field and D is a finite-dimensional central division F-algebra with square free index, then K ₂ D is always generated by the Steinberg symbols {a, b} with a ∈ F*, b ∈ D*. Finally, the tame kernels of central division algebras over F are expressed explicitly.     

套代数上自同构的刻画

本文给出套代数上保零积或者保多项式零化线性映射的刻画,从而得到其上自同构的一些新特征和原子套代数上保零积可加映射的完全分类.     

整系数射影么模羣的自同构

<正> §1.序言 以表行列式之值为±1的n×n整系数矩陣所組成的乘法羣,而以表中行列式之值为+1的矩陣所組成的子羣.的中核由{I,-I}所組成(I是单位矩阵).以表对其中核的商羣,称之为的射影羣.当n是偶数吋,的中核也是由{I,-I}所組成,以表对其中核之商羣,称之为整系数射影模羣. 华罗庚教授和I.Reiner在[1]中决定了,及(m≥1)的自同构.当n是奇     

一类模李代数的导子代数(英文)

本文通过构造一类模线状李代数,求出了它的导子代数,并且证明这个导子代数是可解但不完备的模李代数.这将有利于研究一般模线状李代数的结构.     

套代数上自同构的刻画

本文给出套代数上保零积或者保多项式零化线性映射的刻画,从而得到其上自同构的一些新特征和原子套代数上保零积可加映射的完全分类.     

IDEALS OF TENSOR PRODUCTS OF DIVISION ALGEBRAS AND PRIMITIVE ALGEBRAS

In this paper some lattice isomorphism theorems about one-sided and two-sided ideals intensor products of primitive algebras and division algebras are proved.     

偏代数族的积偏代数

定义了一族偏代数物积偏代数的概念，且对偏代数间的同态映射，由同态映射诱导的合同关系及由同态映射和合同关系诱导的合同关系与积偏代数一起作了深入的讨论，分别得到了一些有意义的结果。     

L-fuzzy代数的刻画

鉴于[2]中已有fuzzy代数结合的不理想，谷文祥和卢荼在L－fuzzy集论中重新定义了L－fuzzy代数，得到了一些理想的结论。但却没有给出它的截集式刻画。本文的目的就是借助于L－fuzzy集的几种水平截集给出了它的几个等价刻画，使得它的表现更为直观且更便于应用。最后，作为应用，本文简洁地证明了L－fuzzy代数在代数同态下是不变的和逆不变的。     

DEGENERATION OF SEMISIMPLE ALGEBRAS

Some observations and conjectures concerning finite dimensional associative commutative algebras that are degenerations of semisimple algebras.

“…on sait qu'on ne sait rien sur cette sorte d'algèbre.” André Weil     

EQUIVALENCE OF x-HOPF ALGEBRAS

Some basic properties of the antipode of an N0I-graded x-Hopf algebra are studied. Also, several equivalent conditions of an N0I-graded x-bialgebra (x-Hopf algebra) are given.