非半单李代数的包络代数及其量子代数在数学和物理学中有重要的应用。本项目致力于研究一些非半单李代数的包络代数及其相应的量子代数的素理想，本原理想和不可约表示的分类。我们将应用非交换环论中的经典方法，如局部化和维数理论等，发展新的技巧和工具， 目标是得到所研究代数的素理想，本原理想的完全分类以及某些重要类型的不可约表示的完全分类。我们期望通过本项目的研究为非半单李代数及其量子代数的无穷维表示提供新的方法。

Non-semisimple Lie algebras and quantum algebras have many important applications in mathematics and physics. In this project, we are concerned about the prime ideals, primitive ideals and classifications of irreducible representations of some enveloping algebras and quantum algebras of non-semisimple Lie algebras. Classical ring theoretic methods will be used extensively in the research, such as localization and dimension theory, to develop new techniques and tools. The main aim of the project is to obtain complete classifications of prime and primitive ideals and certain important families of irreducible representations. This project may provide new methods for the study of infinite dimensional representations of non-semisimple Lie algebras and quantum algebras.