李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

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.     

SOME RESULTS OF MODULAR LIE SUPERALGEBRAS

In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.     

TOWERS OF DERIVATION FOR LIE RINGS AND SOME RESULTS ON COMPLETE LIE RINGS

The well-known tower theorem of groups （resp. Lie algebras） shows that the tower of automorphism groups （resp. derivation algebras） of a finite group （resp. a finite dimensional Lie algebra） with trivial center terminates after finitely many steps. We generalize these results for Lie rings, and present some necessary and sufficient conditions for Lie rings to be complete.     

THE BANACH-LIE GROUP OF LIE TRIPLE AUTOMORPHISMS OF AN H^＊-ALGEBRA^＊

We study the Banach-Lie group Ltaut(A) of Lie triple automorphisms of a complex associative H*-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder(A), are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut(A)0 = Aut(A) implying Ltder(A) = Der(A). In the finite-dimensional case Ltaut(A)0 is a direct product of Aut(A) and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.     

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.     

可换环上一般线性李代数的李三导子

本文研究了含幺可换环上一般线性李代数的李三导子.通过构造特殊矩阵并利用这些矩阵进行运算,得到了任意含幺可换环上一般线性李代数的任意一个李三导子的具体形式,从而推广了导子的概念.     

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.     

Lie comodules and the constructions of Lie bialgebras

In this paper,we first give a direct sum decomposition of Lie comodules,and then accord- ing to the Lie comodule theory,construct some(triangular)Lie bialgebras through Lie coalgebras.     

交换环上严格上三角矩阵的广义李三导子(英文)

本文研究了交换环R上所有n×n严格上三角矩阵构成的李代数N(n,R)(n≥5)上广义李三导子.利用矩阵技巧,证明了N(n,R)(n≥5)上任意广义李三导子为一李三导子与一位似映射的和.对于N(n,R)(n≥3)上广义李导子,得出类似结果.     

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．     

DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS

ABSTRACT

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension.     

EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS

In recent years the Lie superalgebras have become a 8ubject of intere8t in both mathematicsand physic8[']--[41. We know that the embedding theorems of Z-graded Lie superalgebras andfiltered Lie superalgebras play an important role in the investigation of Lie superalgebras. Theembedding theorem of Z-greded Lie superalgebras is already proved in paper [5l. In this paperthe homomorphic realization Of Lie superalgebras is given and proved by tlle method of tlieReff6]. Using the result of honro…     

Generalized Fuzzy Lie Ideals of Lie Algebras

In this paper we introduce new generalized fuzzy Lie ideals of Lie algebras and study some of their important properties.We characterize these generalized Lie ideals of Lie algebras by their level subsets.Some characterization of the generalized fuzzy Lie ideals of Lie algebras are also established.     

与广义Cartan K型李代数有关的一类无限维李代数

本文主要引入了一类与广义Cartan K型李代数有关的无限维李代数,并讨论了 它的单性及任两个这类李代数的同构问题.     

ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.     

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…     

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．     

The Core of a Locally Extended Affine Lie Algebra

Locally extended affine Lie algebras are a general version of extended affine Lie algebras. In this article, we completely describe the structure of the core of a locally extended affine Lie algebra. We prove that the core of a locally extended affine Lie algebra is a direct limit of Lie tori.     

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.