仿射Kac-Moody代数、量子代数和顶点代数均是近几十年来李理论中被广泛研究的领域和方向，其内容涉及到数学和物理的许多关键分支，并且相互之间联系密切。高维仿射李代数是仿射Kac-Moody代数的自然推广，它由物理学家引进之后就成为李理论研究的一个热门领域。本项目旨在通过发展高维仿射李代数与量子代数、顶点代数之间的内在联系来研究这三类代数的结构和表示理论中的一些重要课题。一方面，我们希望借鉴仿射Kac-Moody代数、量子仿射代数和仿射顶点算子代数之间已有的深刻联系来研究高维仿射李代数的量子化和可积表示分类等结构和表示理论。另一方面，由于高维仿射李代数具有一些仿射Kac-Moody代数所没有的性质，我们希望利用高维仿射李代数的这些独特性质来促进量子Kac-Moody代数的扭量子仿射化理论和顶点代数的拟模理论等课题的发展。

Affine Kac-Moody algebras, quantum algebras and vertex algebras are three important classes of algebras in Lie theory, which have profound applications to mathematics and physics. As a natrual generalization of affine Kac-Moody algebras, the notion of extended affine Lie algebras was first introduced by physicsts.Since then the theory of extended affine Lie algebras has been intensively studied for the past twenty years. The present project intends to make deeper investigations on extended affine Lie algebras, quantum algebras, vertex algebras and their mutual relations. On the one hand, we want to study the quantinazation theory and the integrable representation theory for extended affine Lie algebras by using the natural connections among affine Kac-Moody algebras, quantum affine algebras and affine vertex operator algebras. On the other hand, since extended affine Lie algebras allow many more possibilities and hence possible applications than affine Kac-Moody algebras, we hope that some of results on the theory of extended affine Lie algebras can be used to promote the development of the twisted quantum affinization theory for quantum Kac-Moody algebras and the quasi module theory for vertex algebras.