包络代数

令U（D）是D的泛包络代数。

Let U ( D ) be the universal enveloping algebra of the Lie algebra spanned by D.

一类Witt代数的包络代数的表示

Representations of the Enveloping Algebra of the Witt Algebra

量子化包络代数及其有限维商小量子群是一类非常重要的PointedHopf代数。

The quantized enveloping algebras and their finite dimensional quotients , i.e. , small quantum groups , are a class of pointed Hopf algebras which are very important and typical .

τ-李代数的普遍包络代数及其PBW定理

The Enveloping Algebras of τ - Lie Algebras and Their PBW Theorem

通常所谓的量子包络代数可以在经典Poisson括号的意义下实现，以谐振子系统为例，给出Uq（SU（2））的这种经典实现，指出这种q变形伴随着相空间复坐标的Beltrami变形。

We point out that the usual quantum enveloping algebra can be realized at classical level in the sense of Poisson bracket . As an example , we give the classical realization of Uq ( SU ( 2 )) by a system of classical harmonic oscillators .

关于量子普适包络代数变形振子表示的若干讨论

Some Remarks on the Deformed Oscillator Representaton of the Quantum Universal Enveloping Algebra

对具有泛包络代数结构的量子力学控制系统，研究了泛包络代数的可扩张性和系统状态的定义域问题。

For quantum mechanical control systems with structures of universal enveloping algebras , the thesis studies the enlargability of the universal enveloping algebras and the domain problems .

基于描述量子力学系统对称性的李代数结构，本文证明该李代数的泛包络代数提供了足够大的一类控制哈密顿量，因而可以在其上建立量子力学控制系统的模型。

Based on the Lie algebra that describes the symmetries , it is proved in this dissertation that a sufficiently large class of control Hamiltonians can be provided by the universal enveloping algebra of the Lie algebra , on which the quantum mechanical control systems can be modelled .