本项目研究有理顶点算子代数的结构与表示理论。有理顶点算子代数对广义Moonshine猜想的研究具有重要的意义。我们主要研究以下三个方面的问题：一是关于顶点算子代数的orbifold理论。拟重点研究顶点算子代数的置换orbifold理论，将围绕置换orbifold顶点算子代数的twisted模及其fusion product展开研究。二是关于与Moonshine顶点算子代数密切相关的Ising向量的研究。将重点研究两个及多个Ising向量生成的顶点算子代数的结构与表示。三是关于顶点算子代数的有理性，正则性及C_2-余有限性之间的联系。拟围绕“有理性等价于正则性”这个猜想展开研究。

This proposal studies structure and representation of rational vertex operator algebra. Rational vertex operator algebras play important roles in the study of the genralized Moonshine conjecture. We will focus on the following directions. The first direction is about orbifold thoery of vertex operator algebra. We will focus on permutation orbifold theory. In particular, we will study twisted modules of permutation orbifold vertex operator algebra and its fusion products. The second direction is about Ising vectors of vertex operator algbra, which are closely related to Moonshine vertex operator algebra. In particular, we will study structure and representation of vertex operator algebras generated by two or more Ising vectors. Thirdly, we will study connection among rationality, regularity and C_2-cofiniteness of vertex operator algebras. We will mainly study the conjecture that "rationality is equivalent to regularity".