Mathematical Sciences: Lie Algebras and Vertex Operator Algebras

本课题主要研究李代数和顶点算子代数。主要研究人员计划通过从单列和Virasoro代数理论的角度研究顶点算子代数来寻找Rogers-Ramanujan恒等式的经典证明和Lie理论证明之间的联系。此外，他们还将研究怪物月光，并寻找素性李代数上的结构定理，这将简化分类定理的证明。所支持的研究涉及李代数的表示理论，并且集中在这些代数的结构和这些代数在理论物理问题上的应用。从Lie、Killing和Cartan的著作开始，有限维李代数理论在过去的100年里得到了发展，并为每一位数学家和物理学家提供了必要的背景。

This project is concerned with Lie algebras and vertex operator algebras. The principal investigators plan to find relations between the classical and Lie theoretic proofs of the Rogers-Ramanujan identities by studying vertex operator algebras from the viewpoint of monodromy and Virasoro algebra theory. In addition, they will study Monstrous Moonshine and look for structure theorems on Lie algebras of prime characteristic which will simplify the proof of the classification theorem. The research supported concerns the representation theory of Lie algebras and is focused on both the structure of these algebras and the applications of these algebras to questions in theoretical physics. Beginning with works of Lie, Killing, and Cartan, the theory of finite-dimensional Lie algebras has been developed for the past 100 years and provides a necessary background for every mathematician and physicist.