本项目主要研究有理顶点算子代数的形变与量子化。主要内容包括以下两部分：1、有理顶点算子代数在顶点算子代数范畴中的形变理论。 我们将研究格顶点算子代数在顶点算子代数范畴中的形式形变，并进一步研究一般的有理顶点算子代数在顶点算子代数范畴内的形式形变，目标是证明有理顶点算子代数在顶点算子代数范畴中不存在非平凡的形式形变的猜想。2、格顶点算子代数的量子化理论。 我们将利用量子仿射代数以及中心扩张的双杨氏代数的顶点算子表示理论，构造和研究与之对应量子顶点算子代数。目标是构造和研究一般格顶点算子代数的量子化理论。

In this project, we will study the deformation theory and quantization theory of rational vertex operator algebras. The main purpose of this project contains two parts: 1. The deformation theory of rational vertex operator algebras in the category of vertex operator algebras. We will study the formal deformation of lattice vertex operator algebras in the category of vertex operator algebras. Furthermore, we will study the formal deformation of general rational vertex operator algebras. The goal is to prove a conjecture that rational vertex operator algebras are rigid in the sense of formal deformation in the category of vertex operator algebras. 2. The quantization theory of lattice vertex operator algebras. We will use the results of vertex operator representation theory of quantum affine algebras and central extension of double Yangians to construct and study the associated quantum vertex operator algebras. The goal is to construct and study the quantization of general lattice vertex operator algebras.