一类无限维李代数的同构与单性

探讨了一类的无限维李代数,并构造了此类李代数的理想,同构,同态,并对其性质作了探讨.     

整环上二阶线性李代数的自同构

设Ｒ是有１的交换环，２是Ｒ的单位．本文决定了Ｒ上李代数ｓｌ２（Ｒ）的理想．进而，若Ｒ是整环，本文决定了ｓｌ２（Ｒ）与ｇｌ２（Ｒ）的自同构形式．     

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．     

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Heisenberg n-李代数的自同构群(英文)

本文主要研究Heisenberg n-李代数的结构.给出了一类(3m+1)-维Heisenberg3-李代数及(nm+1)-维Heisenberg n-李代数的自同构群.且给出了自同构的具体表达式.     

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。     

多项式代数的一类新的试验多项式 *

域上多项式代数K[ X ]中的一个多项式p称为试验多项式 ,如果代数K[ X]的每个固定p的自同态必为自同构 .给出了一类新的试验多项式 ,可识别多项式代数的非线性自同构 .对于域K的特征为奇素数的情形 ,构作了可识别非半单自同构的试验多项式 .     

一类李代数的结构

本文给出了复数域Ｃ上具有有限多个理想的有限维非可解李代数的结构为Ｌ＝Ｃｒ○＋Ｎ○＋Ｓ，其中Ｓ是Ｌ的Ｌｅｖｉ因子，Ｎ是Ｌ的幂零根基，Ｃｒ○＋Ｎ是Ｌ的根基，ａｄｒ是Ｎ的半单纯线性变换，［ｒ，Ｓ］＝０；还给出了这类李代数的一些重要性质．     

一类只有两个不同非零交换理想的无限维李代数

构造了一类无限维李代数,它是无中心的Virasoro李代数的推广,且只有两个不同的非零交换的理想.还研究了这类李代数的理想、中心和子代数.     

交换半环上的半Leibniz代数

在交换半环上定义半Leibniz代数,给出了半Leibniz代数的理想和商代数,研究了半Leibniz代数的同态和相关结论;利用半Leibniz代数的同余关系,得到半Leibniz代数的商代数的一个同构定理。     

The derivation Lie algebra of the higher rank Virasoro-like algebra and its automorphism groups

In this paper, we study the derivation Lie Algebra of the higher rank Virasoro-like algebra. We prove that it isomorphic to the skew derivation Lie Algebra. We also characterize the automorphism groups of the higher rank Virasoro-like algebra and the skew derivation Lie Algebra. This generalizes the result of some related references.     

The automorphism group of the rank 2 Lie algebra free in the variety \mathfrak{A}\mathfrak{N}_2

We study the location of some finite subgroups in the automorphism group of the rank 2 Lie algebra free in the variety $\mathfrak{A}\mathfrak{N}_2 $ .     

A Lie algebra containing four parameters for the generalized Dirac hierarchy

A Lie algebra containing four parameters is obtained, whose commutation operation is concise, and the corresponding computing formula of constant γ in the variational identity is presented in this paper. As application, a new Liouville integrable hierarchy which can be reduced to Dirac hierarchy is derived by designing a special isospectral problem. We call it generalized Dirac hierarchy.     

On Lie ideals with generalized derivations

Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∈ R and [a, f(U)] = 0 then a ∈ Z or d(a) = 0 or U ? Z; (ii) If f ²(U) = 0 then U ? Z; (iii) If u ² ∈ U for all u ∈ U and f acts as a homomorphism or antihomomorphism on U then either d = 0 or U ? Z.     

Vanishing and cocentralizing generalized derivations on Lie ideals

Let R be a prime ring of characteristic different from 2, U its right Utumi quotient ring, C its extended centroid and L a not central Lie ideal of R. Suppose that F, G and H are generalized derivations of R, with F≠0, such that F(G(x)x?xH(x)) = 0, for any x∈L. In this paper we describe all possible forms of F, G and H.     

Nonzero level Harish-Chandra modules over the Virasoro-like algebra

In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra.     

Construction of generalized thermodynamic potentials by the Lie algebra method

Institute of Physics, Ukrainian SSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 81, No. 2, pp. 239–246, November, 1989.     

A Monster Lie algebra?

This paper defines a remarkable Lie algebra of infinite dimension and rank, and conjectures that it may be related to the Fischer-Griess Monster group.