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.     

关于齐性有界域的同构

<正> n 维复数空间 C_n 中齐性有界域(?)_1到(?)_2上的解析同胚称为同构.当(?)_1=(?)_2,此同构称为自同构.关于齐性有界域在同构下的分类,证明了齐性有界域(?)上有一单可递自同构群 G(?),其 Lie 代数(?)的附属表示的特征根皆实(也见).本文直接从此性质出发,证明了齐     

非单W和S型李超代数的滤过和分类

设F是特征p3的域,g是F上外代数与有限维广义Witt李代数或特殊李代数的张量积所构成的有限维非单李超代数.本文通过确定ad幂零元的方法证明了g的标准滤过是g的自同构群的不变量,进而证明了定义这类李超代数的参数组是内蕴的,从而给出了这两类李超代数在同构意义下的分类.     

量子环面上一类导子李代数的结构和自同构群

本文研究量子环面上的一类导子李代数,它包含了Virasoro-Like代数及其q类似.首先证明了这类导子李代数之间的同构一定是分次同构,并进一步给出了代数同构的充要条件及同构映射的具体表达式,最后确定了该类李代数的自同构群.     

Heisenberg李(超)代数的自同构群

本文研究了Heisenberg李(超)代数的自同构群.利用Heisenberg李(超)代数与线性李(超)代数之间的同构,获得了Heisenberg李(超)代数的自同构群的子群,包括内自同构群、中心自同构群、对合自同构群.     

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     

一类无限维半单李代数

研究了秩为2的Witt型的李代数W2的子代数g1,讨论其同态,同构,核的性质.证明了g1为无限维半单李代数.     

容许二维线性群作用点本原的二弧传递图

一个图称为本原的如果它的自同构群作用在点集上是本原的.在这篇文章里,我们不但完全分类了容许一类二维线性群作用点本原的2-弧传递图,而且决定了他们的自同构群,并在同构意义下决定了它们的个数.     

量子环面上一类导子李代数的结构和自同构群

本文研究量子环面上的一类导子李代数,它包含了Virasoro-Like代数及其q类似．首先证明了这 类导子李代数之间的同构一定是分次同构,并进一步给出了代数同构的充要条件及同构映射的具体表达 式,最后确定了该类李代数的自同构群．     

The general and special superalgebras of formal vectorfields

The natural filtrations of the general algebra W and the special algebra S of formal vectorfields are proved to be invariant. Furthermore, the automorphism groups of W and S are proved to be isomorphic to the corresponding admissible automorphism groups of the base superalgebra U. Then the automorphisms of W or 5 can be induced by the continue automorphisms of U.     

一类量子环面李代数的自同构群

=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数．本文研究李代数L_q=DerA的自同构群Aut L_q．     

一类基于量子环面非交换结合代数的模

在量子环面[1]上构造一类非交换结合代数AQ-模M(a,b),我们还刻划了AQ-模的结构并揭示[2]一类商模序列:每个商模Mn(a)/Mn+1(a)都同构于M(a,0),每个商模的自同构群AutMn(a)/Mn+1(a)均与C*同构.     

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A) for a cluster algebra A and the group AutMn(S) for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.     

Cluster automorphism groups of cluster algebras with coefficients

We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. We introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e., the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.     

The derivation algebra of the associative algebra C q [X,Y,X -1,Y -1] *

The derivation algebra Lof the associative algebra C_q[X,Y,X ^-1,Y ^-1] (q ⁿ :≠1,n∈ N)and the automorphism group Aut Lof L are given.     

On Commuting Automorphisms of Some Finite p-Groups

Mathematical Notes - Let G be a group and Aut(G) be its automorphism group. An automorphism α of G is called a commuting automorphism if α(x)x = xα(x) for all x ∈ G. The set of...     

AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS

61. IntroductionLet G be a trite grouP and S a subs6t of G such thst 1' S and S = S--1. The Cayleygraph X = Cay(G, S) Of G with respect to S is defined to have vertex set V(X) = G and edgeset E(X) = {(g, ag) I g E G, s E' S}. ~ the defection the following two faCts are obvious:(1) the automorphism group Ant(X) of X contains GR, the right regular representation ofG, as a subgroup, and (2) X is cormected if and only if S generates the group G.FOr a Cayley graph X = Cay(G, S) Of …     

Automorphisms of quasitriangular algebras

The outer automorphism group of a nest algebra is canonically isomorphic to the (spatial) automorphism group of the nest itself. The outer automorphism group of the associated quasitriangular algebra is canonically isomorphic to a group of “approximate” automorphisms of the nest. A simple proof that every derivation of a quasitriangular algebra is inner is obtained as a corollary.     

关于有限Abel p-群的自同构群

从有限Abel p-群P的型不变量出发,给出了其自同构群AutP的阶的计算公式,并利用|AutP|的计算公式得到了下面3个结果:1.由有限Abel p-群的型不变量的两种变换得到了其自同构群的阶的变化规律;2.用群的阶、秩、幂指数三个量界定了有限Abel p-群的自同构的阶;3.对部分Frattini子群为p阶群的有限p-群,确定了其自同构群的阶何时达到最小值和最大值.