TKK代数的分次自同构群

$A_{1}$型扩张仿射Lie代数的分类依赖于从Euclid空间中的半格构造得到的TKK代数. Allison等从${\mathbb {R}}^{\nu}(\nu\geq1)$的一个半格出发, 定义了一类Jordan代数. 然后通过所谓的Tits-Kantor-Koecher方法构造出TKK代数${\cal{T}}({\cal J}(S))$, 最后得到$A_{1}$型扩张仿射Lie代数. 在${\mathbb{R}}^{2}$中, 只有两个不相似的半格$S$和$S’$, 其中$S$是格而$S’$是非格半格. 本文主要研究TKK代数${\cal{T}}({\cal J}(S))$的${\mathbb {Z}}^{2}$-分次自同构.     

Tits-Kantor-Koecher李代数的Wakimoto表示

每一个Jordan代数都对应了一个Tits-Kantor-Koecher李代数．在扩张仿射李代数的分类中[1],A_1型李代数的分类依赖于欧氏空间上半格给出的Tits-Kantor-Koecher李代数．另外在相似的意义下,二维欧氏空间R~2中只有两个半格．设S是R~2上的任一半格,T(S)为半格S对应的Jordan代数,G(T(S))为相应的Tits-Kantor-Koecher李代数．利用Wakimoto自由场的方法给出李代数G(T(S))的一类顶点表示．     

Tits-Kantor-Koecher李代数的Wakimoto表示

每一个Jordan代数都对应了一个Tits-Kantor-Koecher李代数.在扩张仿射李代数的分类中[1],A1型李代数的分类依赖于欧氏空间上半格给出的Tits-Kantor-Koecher李代数.另外在相似的意义下,二维欧氏空间R2中只有两个半格.设S是R2上的任一半格,Τ(S)为半格S对应的Jordan代数,(g)(Τ(S))为相应的Tits.Kantor-Koecher李代数.利用Wakimoto自由场的方法给出李代数(g)(Τ(S))的一类顶点表示.     

一个Lie代数的子代数及其相关的两类Loop代数

本文构造了Lie代数A2的一个子代数A2,通过选取恰当的基元阶数得到相应的一个loop代数A2,由此设计一个等谱问题,利用屠格式得到了一个新的Liouville可积的Hamilton方程族.作为其约化情形,得到了一个非线性有理分式型演化方程.再由一个矩阵变换,得到了换位运算与A2等价的Lie代数A1的一个子代数A1,将A1再扩展成一个新的高维loop代数G,利用G获得了所得方程族的一类扩展可积系统.     

互补可换Lie代数

若L是有限维非幂零Lie代数,J（L）＝∞／∩／i=1L^i,称为互补可换Lie代数,如果J（L）与L的Cartan子代数是可换的,且L的每一真理想均包含J（L）。本完全刻划了代数闭域与实数域上互补可换Lie代数的特征。     

具有共变对称张量场的仿射超曲面

用活动标架法从不同方面证明并推广了文[2]的结果：（1）若Mn（n≥2）是n＋1维仿射空间An 1中非退化的仿射超曲面，则2S共变对称（或R·S=0），当且仅当M是仿射球；（2）若Mn（n≥2）是An 1中非退化的仿射起曲面，则K共变对称当且仅当M是仿射球；若K和K都共变对称，则M是仿球，且J=0和仿射度量G是Einstein度量．     

The Frattini Subalgebra of Restricted Lie Superalgebras

In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is a p-ideal of L. We then obtain two results： F（L） = Ф（L） = J（L） = L if and only if L is nilpotent; Fp（L） and F（L） are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.     

关于图的距离标号问题

图G的L（2，1）-标号是一个从顶点V（G）集到非负整数集的函数f（x），使得若d（x，y）：1，则｜f（x）-f（y）｜≥2；若d（x，y）=2，则｜f（x）-f（y）｜≥1。图G的L（2，1）-标号数A（G）是使得G有max{f（v）：v∈V（G）}=k的L（2，1）-标号中的最小数愚。本文将L（2，1）-标号问题推广到更一般的情形即L（d1，d2，d3）-标号问题，并得出了复合图的λd1，d2，d3（G）的上界。     

图的笛卡儿积的测地数

对于图G内的任意两点u和v，u-v测地线是指u和v之间的最短路．I（u，v）表示位于u-v测地线上所有点的集合，对于．S∈V（G），I（S）表示所有I（u，v）的并，这里“u,v∈．S．G的测地数g（G）是使I（S）=V（G）的点集．S的最小基数．在这篇文章，我们研究G×K3的测地数和g（G）与g（G×K3）相等的充分必要条件，还给出了T×Km和Cn×Km的测地数，这里T是树．     

哈密顿线图的一个新结果

设G是一个简单图,G1∈G,G1在G中的度定义为d（G1）=∑v∈V（G）d（v）,其中d（v）为v在G中的度数．主要结果是：设G是n≥3阶几乎无桥的简单连通图,且G≠K（1,n-1）、Q1和Q2,若对G中任何同构于四个顶点路的导出子图I,有d（I）≥2n-6,则G有一个D-闭迹,从而G的线图L（G）是哈密顿图．     

Jordan bialgebras and their relation to Lie bialgebras

We develop the notion of Jordan bialgebras and study the way in which such are related to Lie bialgebras. In particular, it is shown that if a Lie algebra L(J) obtained from a Jordan algebra J by applying the Kantor-Koecher-Tits construction admits the structure of a Lie bialgebra, under some natural constraints, then, J permits the structure of a Jordan algebra. Supported by RFFR grant No. 95-01-01356 and by ISF grant No. RB 6300. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 3–25, January–February, 1997.     

Algebras of Quotients of Jordan–Lie Algebras

In this article, we introduce the notion of algebra of quotients of a Jordan–Lie algebra. Properties such as semiprimeness or primeness can be lifted from a Jordan–Lie algebra to its algebras of quotients. Finally, we construct a maximal algebra of quotients for every semiprime Jordan–Lie algebra.     

Enumerative geometry of triangles,II

An important tool in the study of a finite dimensional Jordan algebra J is the generic norm N of J. N can be introduced as the exact denominator for the inversion map [B&;K, p.761. The norm is of interest because it tests invertibility and it is a semi-invariant for both the structure Lie algebra and the structure group of J.     

The Lie algebra of skew-symmetric elements and its application in the theory of Jordan algebras

We prove that the Lie algebra of skew-symmetric elements of the free associative algebra of rank 2 with respect to the standard involution is generated as a module by the elements [a, b] and [a, b]³, where a and b are Jordan polynomials. Using this result we prove that the Lie algebra of Jordan derivations of the free Jordan algebra of rank 2 is generated as a characteristic F-module by two derivations. We show that the Jordan commutator s-identities follow from the Glennie-Shestakov s-identity.     

一类量子环面李代数的泛中心扩张

设Cq=Cq[x1^±1,x2^1]为复数域上的量子环面,其中q≠0是一个非单位根．D（Cq）为Cq的导子李代数．记Lq为Cq＋D（Cq）的导出子代数．本文研究李代数Lq的泛中心扩张．     

Zur konstruktion von Lie-Algebren aus Jordan-Tripelsystemen

In this paper we study certain Lie algebras which are constructed from the (-1)-eigenspaees of an involution of a Jordan algebra. The construction is a generalisation of the Koecher-Tits-construction. We give necessary conditions in terms of the Jordan algebras for the Lie algebras being simple. If the (-1)-spaces are Peirce-1/2-components then we obtain a close relation between the Lie algebras under consideration and the structure algebras of Jordan algebras. We finally give a list of those types of simple Lie algebras which can be formed by this construction; among them are Lie algebras of type E₆ and E₇.Of fundamental importance for our considerations is a close connection between the constructed Lie algebras and the standard imbeddings of Lie triple systems.     

Prime Quotients of Jordan Systems and Lie Algebras

We show that, unlike alternative algebras, prime quotients of a nondegenerate Jordan system or a Lie algebra need not be nondegenerate, even if the original Jordan system is primitive, or the Lie algebra is strongly prime, both with nonzero simple hearts. Nevertheless, for Jordan systems and Lie algebras directly linked to associative systems, we prove that even semiprime quotients are necessarily nondegenerate.     

树按Balaban指标的排序(英文)

连通图G的Balaban指标(也称J指标)定义为J=J(G)=(|E(G)|)/μ+1∑_(uυ∈E(G)),其中σ_G(u)=∑(w∈V(G)d_G(u,w)此处μ是基圈数.Balaban指标常用于各种QSAR和QSPR的研究.本文根据Balaban指标的计算公式及文中提到的变换方式,我们得到了一些序关系.基于这些序关系,我们确定了n个顶点的树中具有最小Balaban指标的前21个树.     

Dual Coalgebras of Jordan Bialgebras and Superalgebras

W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras.