Mathematical Sciences: Vertex Operator Algebras and their Relations with Posisson Lie Algebras

9616630李本基金资助李教授研究顶点算子理论中的各种问题。他希望证明某些24次全纯顶点算子的存在，研究一些w -代数的合理性，并从顶点代数范畴和泊松李代数范畴建立一个等价函子。这是一项从代数领域开始的研究，但它超越了代数领域，触及了数论和理论物理。产生这些联系的原因是，代数可以被认为是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是现代物理规范场理论广泛使用代数的这一领域，本项目将详细研究其中的一些联系。它还与编码理论和跨通信线路的数据传输有关。

9616630 Li This grant supports the research of Professor H. Li to work on various problems in the theory of vertex operators. He wishes to show that certain holomorphic vertex operators of degree 24 exist, to work on the rationality of some W-algebras and to establish an equivalent functor from the category of vertex algebras and the category of Poisson Lie algebras. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.