关于完满的Lie超代数

In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.     

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。     

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.     

泛阶化李超代数

对于给定的负阶化李超代数K-,本文定义了K-型泛阶化李超代数并证明了它的存在性．进而引出阶化Cartan型李超代数,并且证得阶化Cartan型李超代数 W(m,n),K(m,n,ωA),S(m,n)和H(m,n)分别可以用某种泛阶化李超代数来刻画．     

Quadratic Lie Superalgebras Generalized by Balinsky–Novikov Superalgebras

Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Virasoro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2|2 to be a quadratic Lie superalgebra.     

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.     

A Sufficient and Necessary Condition for a Solvable Lie Algebra to Be Complete

In this paper,we give a sufficient and neccesary condition under which a solvable Lie algebra is complete.     

Completeness of quasi-filiform Lie algebras

It is proved that for any quasi-filiform of non-zero rank the solvable Lie algebra obtained by adjoining a maximal torus of outer derivations is complete. Further, for any positive integer m, it is shown that there exist solvable complete Lie algebras with the second Chevalley–Eilenberg cohomology group of arbitrary dimension.     

Not all graded identities for Mn(E) come from Mn,n

We introduce here two classes of infinite dimensional Lie Algebras called potentially nilpotent and potentially solvable and we define the notion of Fine Lie Algebra. The study of the Fine Lie Algebras allows to obtain their complete classification in the natural or standard graded cases.     

一类模李代数的导子代数(英文)

本文通过构造一类模线状李代数,求出了它的导子代数,并且证明这个导子代数是可解但不完备的模李代数.这将有利于研究一般模线状李代数的结构.     

Algebraic Lie algebras with complete Borel subalgebras

In this article we prove that an algebraic Lie algebra over an algebraically closed field of characteristic 0 is complete if its Borel subalgebras are complete. Thus the study on complete Lie algebras may somewhat be reduced to that on solvable complete ones.     

Completable nilpotent Lie superalgebras

We discuss a class of filiform Lie superalgebras L^n,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0ˉ(L^n,m) and Der1 (L^n,m). By computing a maximal torus on each L^n,m, we show that L^n,m are completable nilpotent Lie superalgebras. We also view L^n,m as Lie algebras, prove that L^n,m are of maximal rank, and show that L^n,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.     

A class of generalized odd Hamiltonian Lie superalgebras

We study class of finite-dimensional Cantan-type Lie superalgebras HO（m） over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO（m）.     

一类广义W型李超代数

构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

一类Weyi型单李超代数

本文研究了单李超代数的构造理论.借助于张量积方法,定义了一类Weyl型结合超代数和一类Weyl型李超代数,并且证明了这类Weyl型结合超代数和Weyl型李超代数是单的充分必要条件.     

线状李超代数Ln,m上的Yang-Baxter 方程

在特征零的代数闭域上,首先做出Ln,m 的一个空间的直和分解,从而将Ln,m 上的Yang-Baxter 方程的解分为若干情形。然后分别在每种情形下对Yang-Baxter 方程进行求解,进而得到了Ln,m 上的所有的Yang-Baxter方程的解的矩阵形式。     

三次可解型非退化李代数及其导子李代数的结构

本文给出了非退化可解李代数的两个类型:三次可解型非退化李代数和扩充的 Heisenberg李代数,并确定三次可解型非退化李代数及其导子李代数的结构．     

The abelian subalgebras of maximal dimensions for general linear Lie superalgebras

Over an algebraically closed field of characteristic zero, all the abelian subalgebras of maximal dimensions for the general linear Lie superalgebras are classified in the sense of conjugation. As a consequence, the minimal faithful representations are determined for the so-called nice abelian Lie superalgebras.