仿射李（超）代数及相关李（超）代数的结构与表示理论

无限维李（超）代数的结构与表示理论在数学和物理学的相关领域中起着非常重要的作用和影响。多数重要的无限维李（超）代数都与仿射李（超）代数密切相关。本项目主要研究仿射李（超）代数及相关李（超）代数的结构与表示理论： 研究量子仿射超代数的 Drinfel'd实现及其表示；研究对偶李（超）双代数的结构；研究 C1 生成的顶点（超）代数的结构； 研究与（超）Virasoro 代数密切相关的几类重要的无限维李（超）代数的结构与表示，包括导子代数、自同构群、上同调群、权模及非权模等。

The structure and representation theory of infinite-dimensional Lie (super)algebras plays an important role in many fields of mathematics and physics. Many important infinite-dimensional Lie (super)algebras are closely related to affine (super)algebras. In this project we will focus on studying the structure and representation theory of affine (super)algebras and related (super)algebras: the Drinfel’d realizations and representations of quantum affine superalgebras; the structures of some Lie (super)bialgebras; structures of C1-generating vertex (super)algebras; the structure and representation theory of some important infinite-dimensional Lie (super)algebras (which are closely related to (super)Virasoro algebras), including derivation algebras, automorphism groups, cohomology groups, weight modules and non-weight modules.