一类带有非退化不变对称双线性函数的幂零李代数

本文证明了一类带有非退化不变对称双线性函数、幂零指数为Ｎ的李代数 满足：定理１．（ｉ）ｃ（ｇ）＝ｇ~Ｎ; （ｉｉ）ｄｉｍｃ（ｇ）＝ｌ．ｌ是ｇ的生成元个数．定理３给出了这类李代数结构的充分且必要条件．     

紧 n -Lie 代数与不变双线性型

该文研究 n -Lie代数的非退化不变双线性型. 给出了实数域上紧 n -Lie 代数的概念, 并对其结构进行了研究.     

一类带有非退化对称不变双线性型的李代数

本文给出了一类带有非退化对称不变双线性型的李代数的特征性质、结构及 实现．     

辛代数的不变双线性型

考察了辛代数和与它相联系的李三系的双线性型之间的关系,并证明了辛代数的反对称不变双线性型可以唯一扩张到与它相联系的李三系中.作为这种关系的一个应用,得到了二次辛代数是单辛代数的一个充要条件,并证明二次辛代数的唯一分解定理.     

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．     

相应于一类对称自对偶李代数的顶点代数结构

设gsp是给定的对称自对偶李代数,给出了相应于gsp的一个顶点代数结构.     

带有非退化不变对称双线性型的有限维可解李代数

本文讨论复数域上带有非退化不变对称双线性型的,可裂的有限维可解李代数的性质及结构.给出了不可分解的非退化可解李代数的定义.证明了本文所讨论的李代数可以分解成不可分解的非退化可解理想的正交直和.对于不可分解的非退化可解李代数,给出了它关于极大环面子代数的根空间分解;讨论了根空间的结构及运算关系;证明了它的 Cartan 子代数的交换性,并给出了 Cartan子代数的结构.     

一类Schrdinger-Virasoro型李代数的量子化

李双代数的量子化是获取新的量子群的重要方法.本文通过Drinfel'd扭元,对一类Schr(o|¨)dinger-Virasoro型李代数进行了量子化,得到了一类既非交换又非余交换的Hopf代数.     

对称自对偶李代数的一些性质

给出了一类带有非退化对称不变双线性型及对称自对偶李代数的分解唯一性的一个充分条件,并讨论此类李代数的特殊性质.     

反李三系的不变双线性型

本文考察了反李三系和它的标准嵌入李超代数的Killing型之间的关系,并且证明了反李三系的反对称不变双线性型可以被唯一地扩张到它的标准嵌入李超代数。作为扩张定理的一个应用,得到了二次李和反李三系的唯一分解定理。     

2-Cocycles of original deformative Schr?dinger-Virasoro algebras

Both original and twisted Schr?dinger-Virasoro algebras, and also their deformations were introduced and investigated in a series of papers by Henkel, Roger and Unterberger. In the present paper we aim at determining the 2-cocycles of original deformative Schr?dinger-Virasoro algebras. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471091, 10671027), Foundation of Shanghai Education Committee (Grant No. 06FZ029) and “One Hundred Talents Program” from University of Science and Technology of China     

Invariant symmetric bilinear forms for reflection groups

In this paper we describe a connection between Vinberg's criterion for the existence of an invariant symmetric bilinear form for a geometric representation of a Coxeter groups and other criteria which are formulated in terms of conjugation invariant sets of reflections generating a given group. Similar methods lead to the result that every non-symmetrizable Kac--Moody Lie algebra contains a non-symmetrizable subalgebra of rank 3. Finally we explain how the results for symmetric bilinear forms can also be obtained for skew-symmetric forms. Received 3 March 2000.     

Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras

We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) are triangular coboundary.     

Topologically left invariant means on semigroup algebras

LetM(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroupS with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions forM(S)* to have a topologically left invariant mean.     

Projections onto invariant subspaces of some banach algebras

In this paper, among other things, the author studies the weak^＊-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.     

A counterexample to a conjecture on flat bilinear forms

We provide a counterexample to a conjecture on the dimension of the nullity of a flat symmetric bilinear form.

     

Quadratic forms for the 1-D semilinear Schrödinger equation

This paper is concerned with 1-D quadratic semilinear
Schrödinger equations. We study local well posedness in classical Sobolev space of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.