CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS

In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reinhardt domains, and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n²-2 (where n is the dimension of domain).     

一类有界对称域上的Hartogs型域的自同构群

本文研究了稍微广泛的一类Hartogs型域的自同构群.利用华域的自同构群,获得了一类有界对称域上的Hartogs型域的自同构群的具体形式,推广了有界对称域上的Hartogs型域的自同构群这一结果.     

有限Abel群的一个特征

本文证明了有限群Ｇ是Ａｂｅｌ群当且仅当Ｇ_ｒ满足下列条件：（Ⅰ） Ｇ有一个幂自同构 ａ使得 ＣＧ（ａ）是一个初等 ＡｂｅｌＺ一群．（Ⅱ）Ｇ没有子群与２－群＜ａ,ｂ｜ａ~２~ｎ＝ｂ~２~ｍ＝１,ａ~ｂ＝ａ~（１＋２）~（ｎ－１）＞同构,其中ｎ≥３,ｎ≥ｍ．利用该结果,作者还证明若有限群Ｇ有一个幂自同构ａ使得Ｃ_Ｇ（ａ）是一个初等Ａｂｅｌ２－群,则Ｇ是幂零群     

2-Local Automorphisms on Basic Classical Lie Superalgebras

Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).     

Commuting holomorphic functions and hyperbolic automorphisms

We give a complete classification of the holomorphic self-maps of the unit ball of into itself which commute with a given hyperbolic automorphism.

     

自由正交模格FMOk(n)的自同构群

文章先利用自同构映射保有限并的性质研究了一般正交模格的次直积的自同构群与自同构群的次直积的关系,再用块置换的方法研究了MOk的自同构群的生成元集,由此得到自由正交模格FMOk(n)的自同构群的直积分解式,从而完全解决了FMOk(n)的自同构群的结构问题.     

LOCAL CHARACTERISTIC OF HOLOMORPHIC AUTOMORPHISM ON CLASSICAL DOMAIMS

§1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　　ＬｅｔＭｂｅａｃｏｍｐｌｅｘｍａｎｉｆｏｌｄ.Ｆｏｒａｎｙｐ∈ＭａｎｄａｎｙＸ∈Ｔ1,0ｐ(Ｍ),ｔｈｅＫｏｂａｙａｓｈｉｉｎｆｉｎｉｔｅｓｉｍａｌｐｓｅｕｄｏｍｅｔｒｉｃ[1]ｏｆＸｉｓＦ(Ｘ):=ｉｎｆ｜ａ｜∈Ｃ,ｆ:ＤＭｓ.ｔ.ｆ(0)=ｐａｎｄｆ(ａｚ)=Ｘ,ｗｈｅｒｅＤｉｓｔｈｅｕｎｉｔｄｉｓｋａｎｄｆ∈Ｈｏｌ(Ｄ,Ｍ)ｉｓｔｈｅｈｏｌｏｍｏｒｐｈｉｃｍａｐｆｒｏｍＤｔｏＭ,ａｎｄｔｈｅＣａｒａｔｈｅｏｄｏｒｙｉｎｆｉｎｉｔｅｓｉｍａｌｐｅｕｓｄｏｍｅｔｒｉｃｏｆＸｉｓＥ(Ｘ):=ｓｕｐ…     

李型群Bn（F）的一组第四类极大子群

用自同构构造了李型群Ｂｎ（Ｆ）的一组第四类极大子群，肯定地回答了第四类极大子群的存在性问题。     

具有一个T．I．Sylow 2-子群的有限群的类保持Coleman自同构

设G是一个有限群,它的Sylow 2-子群是T.I.集,证明了如果G的2的方幂阶类保持自同构在G任意的Sylow子群上的限制等于G的某个内自同构的限制,则它一定是一个内自同构.对这样的自同构的研究是由整群环的同构问题所引起的.     

有限生成自由代数FV（LK）（n）的自同构群（英文）

本文研究了自同构群AutLk和AutFV(LK)(n)的结构问题.利用了正交模格及其自同构群的直积分解方法,获得了正交模格Lk和自由代数FV(LK)(n)的自同构群的直积分解式.     

Line spreads of PG(5, 2)

All line spreads of PG(5, 2) are constructed and classified up to equivalence by exhaustive generation considering the specific properties of the automorphism group, and the participation of the spread lines in the subspaces of dimension 3. There are 131,044 inequivalent spreads. The orders of the automorphism groups preserving the spreads, and the 2‐ranks of the related by Rahilly's construction affine 2‐(64,16,5) designs are also computed. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 90–102, 2009     

第三类超Cartan域的Bergman核函数

显式给出了第三类超Cartan域的Bergman核函数及其全纯自同构群。     

The Bergman Kernel on Cartan-egg Domains of the First Type

Ｉｎ 1 92 1 ,Ｂｅｒｇｍａｎｉｎｔｒｏｄｕｃｅｄａｋｅｒｎｅｌｆｕｎｃｔｉｏｎ ,ｗｈｉｃｈｉｓｎｏｗｋｎｏｗｎａｓｔｈｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎ .ＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｒｅｅｘｉｓｔｓａｕｎｉｑｕｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎｆｏｒｅａｃｈｂｏｕｎｄｅｄｄｏｍａｉｎｉｎＣｎ.ＦｏｒｗｈｉｃｈｄｏｍａｉｎｓｃａｎｔｈｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎｂｅｃｏｍｐｕｔｅｄｂｙｅｘｐｌｉｃｉｔｆｏｒｍｕｌａｓ?Ｔｈｉｓｉｓａｎｉｍｐｏｒｔａｎｔ…     

线性系统的极限跟踪性

给出了Rⁿ上的线性同构和线性流具有极限跟踪性的特征：线性同构具有极限跟踪性当且仅当其对应的矩阵为双曲的;线性流具有极限跟踪性当且仅当其对应矩阵的所有特征根均具有非零实部.     

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.     

半环上的三角矩阵乘法半群的自同构

设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2.     

Gelfand–Kirillov Dimension for Automorphism Groups of Relatively Free Algebras

Using ideas of our recent work on automorphisms of residually nilpotent relatively free groups, we introduce a new growth function for subgroups of the automorphism groups of relatively free algebras Fⁿ(V) over a field of characteristic zero and the related notion of Gelfand-Kirillov dimension, and study their behavior. We prove that, under some natural restrictions, the Gelfand-Kirillov dimension of the group of tame automorphisms of Fⁿ(V) is equal to the Gelfand-Kirillov dimension of the algebra Fⁿ(V). We show that, in some cases, the Gelfand-Kirillov dimension of the group of tame automorphisms of Fⁿ(V) is smaller than the Gelfand-Kirillov dimension of the whole automorphism group, and calculate the Gelfand-Kirillov dimension of the automorphism group of Fⁿ(V) for some important varieties V.Partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.2000 Mathematics Subject Classification: primary 16R10, 16P90; secondary 16W20, 17B01, 17B30, 17B40     

无限亚局部循环群及其自同构群

作为之前工作的继续, 本文研究了无限亚局部循环群的结构以及它们的自同构和自同构群. 设 A,B 分别是秩1 的无挠Abel 群, G 为n 阶循环群. 群E 是A 被G 的扩张, G 被A 的扩张或者A 被 B 的扩张. 讨论了群E 的结构以及它们的自同构, 并得到了它们的自同构群.     

分裂扩张的稳定自同构群

本文给出有限群的分裂的Ａｂｅｌ扩张的稳定自同构群的计算．作为应用,给出了循环群的半直积的自同构群的结构,它包括了若干已知结果,如文［１］的全部结果,并解决了［１］提出的问题．