一些无限维完备李代数

本文讨论了无限维完备李代数的一些性质,由Virasoro代数,Kac-Moody代数构造了几类无限维完备李代数.同时给出了Kac-Moody代数及其广义抛物子代数的导子代数的刻划.证明了完备李代数的Loop扩张仍为完备李代数.     

一些无限维完备李代数

本文讨论了无限继完备李代数的一些性质,由Virasoro代数,Kac－Moody代数构造了几类无限维完备李代数．同时给出了Kac－Moody代数及其广义抛物子代数的导子代数的刻划．证明了完备李代数的Loop扩张仍为完备李代数。     

无限维Heisenberg代数的导子代数和全形

给出了无维Ｈｅｉｓｒｂｅｒｇ代数的全形和全形的导子代数Ｄｅｒ（ｓ）证明（ｓ）不是一个完备李代数，但Ｄｅｒ（ｓ）是一个完备李代数。     

关于完备李群与完备李代数

孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。     

最简线状n-李代数

定义了一类特殊的幂零n-李代数,即最简线状n-李代数,它是最简线状李代数的推广.确定了m维最简线状n-李代数A的导子代数Der(A)和自同构群Aut(A),定义了n-李代数的全形h(A)=Der(A)( ) A,并证明了当A的基域F的特征P为零或P＞m-n时,Der(A)是不可解的完备李代数,而h(A)的一个子代数是可解的完备李代数,当F的特征为零时,Aut(A)是无中心的不可解群.     

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.     

一般扭算子李代数g(G,l)[σ]的结构

扭算子李代数在研究李代数的结构中有着广泛的应用,因而讨论扭算子李代数的结构具有很重要的意义.讨论了随着G,l的选取,在各种情形下扭算子李代数g(G,l)[σ]所具有的代数结构.     

算子李代数g(G,M)[σ]的子代数

在李代数的研究中,经常使用算子李代数的结构去刻划其它李代数的代数结构,由算子构成的李代数在李代数理论中占有重要的位置.构造了算子李代数g(G,M)[σ]的子代数,然后讨论了这些子代数的代数结构.     

由六个顶点的箭图诱导的项链李子代数

无限维项链李代数是新的一类无限维李代数,本文重点讨论了由六个顶点的箭图诱导的项链李子代数,研究了这类李子代数的子代数,同构和同态,这类李代数是Virasoro-like李代数的推广,并讨论了它的其他一些性质.     

Solvable complete lie algebras. I ∗

In this paper, we will discuss the properties of solvable complete Lie algebra, describe the structures of the root spaces of solvable complete Lie algebra, prove that solvable Lie algebras of maximal rank are com-plete, and construct some new complete Lie algebras from Kac-Moody algebras.     

COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS

The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.     

完备Lie代数的若干进展

近十年来，特别是近几年完备Ｌｉｅ代数的研究取得了许多进展，本文分以下六个方面介绍这一领域的研究状况，０）引言；１）完备Ｌｉｅ代数的分解和唯一性；２）一些完备Ｌｉｅ代数。３）可解完备Ｌｉｅ代数；４）完备Ｌｉｅ代数的极大环面子代数，Ｋｉｌｌｉｎｇ型及结构；５）一些公开问题。     

Two Kinds of Solvable Complete Lie Algebras

In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras.     

关于MH中的Lie双代数和余Poisson-Hopf代数

本文研究余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余ＰｏｉｓｓｏｎＨｏｐｆ代数,我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系。     

Generalized Lie Algebras and Cocycle Twists

We use the results of Etingof and Gelaki on the classification of (co)triangular Hopf algebras to extend Scheunert's “discoloration” technique to Lie algebras in the category of (co)modules. As an application, we prove a PBW-type theorem for such Lie algebras. We also discuss the relationship between Lie algebras in the category of (co)modules and symmetric braided Lie algebras introduced by Gurevich. Finally, we construct examples of symmetric braided Lie algebras that are essentially different from Lie coloralgebras.     

关于μ~H中的Lie双代数和余Poisson-Hopf代数(英文)

本文研究余三角 Ｈｏｐｆ代数余模范畴中的 Ｌｉｅ双代数和余 Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数．我们主要讨论余三角Ｈｏｐｆ代数余模范畴中的Ｌｉｅ双代数和余Ｐｏｉｓｓｏｎ－Ｈｏｐｆ代数之间的关系．     

以幂零李代数R_n为幂零根基的可解李代数(英文)

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.     

Zero Divisors in Amalgamated Free Products of Lie Algebras

We introduce the notion of domain for Lie algebras, discuss when the free amalgamated Lie product of two domains is a domain again, classify commuting elements in the free amalgamated product of two Lie algebras and describe the center of this product.     

The Lie Algebras in which Every Subspace s Its Subalgebra

In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.