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.     

特殊Cartan型李超代数的Borel子代数

本文研究了特征零的代数闭域上秩为4的有限维特殊Cartan型李超代数S的结构.利用正则元的划分,确定出S关于典范环面的所有正根系,从而得到了S的所有Borel子代数;对于每一个正根系,通过给出其单根系,得到了任何两个Borel子代数的连接关系;最后确定了每一个Borel子代数的极大可解性.本文所得结果可用于进一步研究Cartan型单李超代数的结构与表示.     

GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) = 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.     

TWISTED CONJUGACY CLASSES IN LATTICES IN SEMISIMPLE LIE GROUPS

Given a group automorphism ?: Γ?→?Γ, one has an action of Γ on itself by ?-twisted conjugacy, namely, g.x?=?gx?(g ^?1). The orbits of this action are called ?-conjugacy classes. One says that Γ has the R∞-property if there are infinitely many ?-conjugacy classes for every automorphism ? of Γ. In this paper we show that any irreducible lattice in a connected semisimple Lie group having finite centre and rank at least 2 has the R∞-property.     

阶化Cartan型李代数的上同调

本文利用广义限制李代数的概念和应用Frobenius代数的一些性质来研究广义限制李代数的广义限制完备上同调,并利用广义限制上同调与通常上同调的关系尝试着给出一种计算系数为不可约模的阶化Cartan型李代数上同调的方法.     

阶化Cartan型李代数的上同调

本文利用广义限制李代数的概念和应用Frobenius代数的一些性质来研究广义限制李代数的广义限制完备上同调,并利用广义限制上同调与通常上同调的关系尝试着给出一种计算系数为不可约模的阶化Cartan型李代数上同调的方法.     

ALGEBRAIC GROUPS ASSOCIATED WITH GRADED LIE ALGEBRAS OF CARTAN TYPE

§０．ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｋｎｏｗｎｔｈａｔｏｖｅｒａｌｇｅｂｒａｉｃａｌｙｃｌｏｓｅｄｆｉｅｌｄｓｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃ０，ｔｈｅｒｅｅｘｉｓｔｓａｇｏｏｄｃｏｒｅｓｐｏｎｄｅｎｃｅｂｅｔｗｅｅｎｔｈｅｃｏｎｎｅｃｔｅｄ...     

与广义Cartan K型李代数有关的一类无限维李代数

本文主要引入了一类与广义Cartan K型李代数有关的无限维李代数,并讨论了 它的单性及任两个这类李代数的同构问题.     

Witt型李超代数偶部的可分解极大阶化子代数

本文研究了Z-阶化Witt型李超代数偶部g=(O)＞-1gi的结构特点,介绍了可分解极大阶化子代数的定义.通过计算,给出g1作为go-模的适当子模序列.利用构造法,确定了g在素特征域上的可分解极大阶化子代数的分类.这有助于进一步了解Witt型李超代数的内在性质.     

COHOMOLOGY OF GRADED LIE ALGEBRAS OF CARTAN TYPE S (n, m)

Let F be an algebraically closed field of characteristic p>3. This paper studies the cohomology of graded Lie algebras S(n,m) of Cartan type over F. The author determines the structures of H~1(S(3,m), _0), where _0 is the graded S(3,m)-module which is induced by an irreducible sl (3)-module V_0, the structures of H~1(S(3,m), V), where V is an irreducible S(3,m)-module, and the structures of the restricted cohomology H_*~1(S(3,(1, 1, 1)), V), where V is an irreducible restricted S(3, (1, 1, 1))-module.     

ON THE PRODUCT OF DIAGONAL CONJUGACY CLASSES*

Let A, B ∈ GL(n, F) be diagonal non-scalar n × n matrices over any field F. It will be discussed under which conditions the product of conjugacy classes of A and B contains all cyclic matrices C with det C = det A det B. A sufficient condition depending on the number of pairwise different eigenvalues of A and B will be formulated.

     

ON THE TOPOLOGICALLY CONJUGATE CLASSES OF ANOSOV ENDOMORPHISMS ON TORI

This paper considers the following question: Given an Anosov endomorphism f on T~m, whether f is topologically conjugate to some hyperbolic total endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. Hwever for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i. e., for generic Anosov endomorphisms, they are not topologically conjugate to any hyperbolic toral endomorphism.     

论有限群元素共轭类的平均长度

本文研究有限群元素共轭类的平均长度问题.利用初等群论方法和有限群特征标理论,在共轭类平均长度为某一定数时,获得了对有限群结构的刻划,且对有限群数量性质的研究是有意义的.     

Cartan型模李超代数W的二阶上同调群H2(W,F)

本文研究了有限维广义Witt李超代数W的二阶上同调群H2(W,F),其中F是一个特征P＞2的代数封闭域.通过计算W到W*的导子,得到H2(W,F)是平凡的.应用此结果,我们可得W的中心扩张是平凡的.