代数

The quantum deformation of a Lie algebra is obtained by adding one parameter q,which is reduced to the original Lie algebra when taking the limit q→1;some properties of the original Lie algebra remain.

在Hopf代数或量子群理论中，构造李双代数的量子化是产生新的量子群的一个十分重要方法，研究李双代数的重要目的之一就是对其量子化。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

In this paper, we mainly study representations of strong semisimple n-Lie algebras, prove that a representation of a strong semisimple n-Lie algebra is a representation of the reductive Lie algebra LP, and the relative properties.

本文主要研究了强半单的n-李代数的表示，证明了强半单的n-李代数的表示可转化为一个约化李代数Lρ的表示，并证明了不变线性形等其它相关性质。

In this paper, we first give the Maschke's theorem of smash product A#H * about semisimple algebra , after studing smash product # definited by Y.

Doi 所定义的Smash 积＃，给出了Smash 积A＃ H＊关于半单代数的Maschke 定理；给出了可分代数与余可分余代数之间的对偶关系。

Symmetry group is semisimple, the system has a fine cascade decomposition that is a qasi-parallel decomposition, which is corresponding to the decomposition of linear systems under the semisimple symmetry algebra.

由于对称代数对线性系统的结构有重要作用，特别是当该代数半单时，系统可分解为多个独立的子系统，因此如何就给定的线性控制系统构造出其对称代数具有重要意义。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

According to the rough structure and algebra structure, the main work is to study the application of rough set theory on algebra system-groups and rings in this thesis. So that rough algebra system is built better perfectly.

本文根据粗糙结构和代数结构，研究了粗糙集理论在代数系统——群、环上的应用，以此建立比较完善的粗糙代数系统。

In this paper,the main work is to extended the premitive model of rough sets;Accorting to the Rough structure and algebra structure,the main work is to study the application of rough set theory on algebra system-group,so that rough algebra system is better perfectly.

本文在现有的Pawlak粗糙集模型基础上，对模型进行推广；根据粗糙结构和代数结构及已有的研究成果的基础上，更进一步地研究了粗糙集理论在代数系统一群上的应用，以此建立较为完善的粗糙代数系统。

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

It is shown that if L is a subalgebra of a Lie color algebra Q, then Q is an algebra of quotients of L if and only if Q is ideally absorbed into L.

利用没有非零零化子的理想对Lie color代数的商代数进行刻画，证明了：若L为Lie color代数Q的子代数，则Q为L的商代数当且仅当Q理想吸收于L。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。