李超代数上的不变双线性型

本文通过定义李超代数上的形心和零次形心来考察其性质.证明了二次李超代数(G,B)上的不变数积的集合和其形心中的可逆B-超对称元素的集合之间存在一一对应.而对实单李超代数分为两种不同的类型:或者是一个忽略了复结构的复李超代数或者是一个复单李超代数的实形式.     

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.     

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…     

MINIMAL SURFACES IN 3—DIMENSIONAL SOLVABLE LIE GROUPS

The author studies minimal surfaces in 3-dimensional solvable Lie groups with left invariant Riemannian metrics. A Weierstraβ type integral representation formula for minimal surfaces is obtained.     

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.     

K型模李超代数的导子代数

设 F是特征数 p>3的域 ,本文通过计算方法决定了 F上有限维 Cartan- type单李超代数 k( m,n,t～)的导子代数 .     

具有非退化亦型的Z—阶化李超代数

本文给出了Ｚ－阶化有限维单李超代数具有非退化亦型的一个必要条件。应用这一结果,我们可以得到Ｃａｒｔａｎ型李超代数Ｘ（ｎ）与Ｘ（ｍ,ｎ,ｔ）的Ｋｉｌｌｉｎｇ型是退化的。     

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.     

Witt型李超代数偶部的可分解极大阶化子代数

本文研究了Z-阶化Witt型李超代数偶部g=(O)＞-1gi的结构特点,介绍了可分解极大阶化子代数的定义.通过计算,给出g1作为go-模的适当子模序列.利用构造法,确定了g在素特征域上的可分解极大阶化子代数的分类.这有助于进一步了解Witt型李超代数的内在性质.     

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.     

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.     

特殊Cartan型李超代数的Borel子代数

本文研究了特征零的代数闭域上秩为4的有限维特殊Cartan型李超代数S的结构.利用正则元的划分,确定出S关于典范环面的所有正根系,从而得到了S的所有Borel子代数;对于每一个正根系,通过给出其单根系,得到了任何两个Borel子代数的连接关系;最后确定了每一个Borel子代数的极大可解性.本文所得结果可用于进一步研究Cartan型单李超代数的结构与表示.     

交换环上一个线性李超代数的导子

本文研究了交换环上一个李超代数的导子.利用构造几类特殊的导子,获得了此李超代数的任意导子是几类特殊导子的和.推广了交换环上李代数的导子.     

Novikov algebras and Novikov structures on Lie algebras

We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any free three-step nilpotent Lie algebra admits a Novikov structure. We study the existence question also for Lie algebras of triangular matrices. Finally we show that there are families of Lie algebras of arbitrary high solvability class which admit Novikov structures.     

The Classification and Realization of Complete Lie Algebras with Commutative Nilpotent Radicals

in this paper, the classification and realization of complete Lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete Lie algebras are obtained.     

Banach空间抽象线性脉冲方程的可解范围

本文在一船Ｂａｎａｃｈ空间Ｘ上研究抽象线性脉冲方程的可解范围，其中Ａ是闭线性算子，文中构造了Ｘ的一个线性子空间Ｖ且在Ｖ上定义范数成为Ｂａｎａｃｈ空间，Ａ限制在Ｖ上生成指数衰减的强连续双半群，从而表明方程在Ｖ上可解，并证明Ｖ是方程可解的极大范围。     

关于局部顶点李代数的一些注记

本文研究局部顶点李代数与顶点代数之间的关系.利用由局部顶点李代数构造顶点代数的方法,定义局部顶点李代数之间的同态,证明了同态可以唯一诱导出由局部顶点李代数构造所得到的顶点代数之间的同态.     

C-Ideals of Lie Algebras

A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B ∩ C ≤ B _L , where B _L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.