本文对对偶扩张代数的性质作了有意义的研究。

In this paper, some useful properties of dual extension algebras are considered.

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半群平移壳理论是半群代数理论的一个重要部分，在半群的理想扩张理论中占有重要地位。

The theory of translational hull of semigroups is an important branch of the algebra theory and plays a basic role in the theory of ideal extensions of semigroups.

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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.

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