本项目对顶点算子代数结构与表示理论中的一些基本问题开展研究。主要研究内容如下： 1. 在前期研究的基础上，继续central charge为1的有理顶点算子代数的分类工作，完成对central charge为1的顶点算子代数的完全分类，有理顶点算子代数的分类是顶点算子代数理论中最重要和最为困难的研究问题之一。2. 对顶点算子代数的twisted表示进行深入研究。给定一个顶点算子代数V和V的一个自同构T，怎样构造出V的T-twisted表示，一直是顶点算子代数理论中没有解决的公开问题。目前甚至对最为简单的二阶自同构，除了几类特殊的顶点算子代数外，都没有一个可行的一般构造办法，我们希望在这方面会有实质性突破。3. 对non-local顶点代数开展研究，特别是量子顶点代数的研究，我们的目标是给出量子顶点代数的好的例子，实现量子仿射代数与量子顶点代数的对应。

This project will study the structure and representation theory of vertex operator algebras and Lie algebras. There will be three major underlying themes in the project. First, we will continue our study on classification of rational vertex operator algebras of central charge 1. Classification of rational vertex operator algebras is one of the most important and hardest questions in the theory of vertex operator algebras. Our goal is to classify all the rational vertex operator algebras of central charge 1. Secondly, we will study twisted representations of vertex operator algebras. Given a vertex operator algebra V and an automorphism T of it with finite order, how to construct T-twisted V-modules has always been an open problem in the theory of vertex operator algebras. Up to now, even for an automorphism of order 2, there is no general method to construct twisted modules, except for a few classes of vertex operator algebras. We expect to make some breakthrough in this field. Finally, this project will study non-local vertex algebras, especially quantum vertex algebras. Our goal is to give good examples of quantum vertex algebras and establish a theory of quantum affine vertex algebras associated to quantum affine Lie algebras.