Vertex Operator Algebras & Lie Algebras

9401851莱波斯基主要研究人员将研究顶点算子代数和李代数。一是研究顶点张量范畴的新概念。另一类是为自由李代数构造一种新的基，并研究某些Cartan型单李代数的素性仿射。他们将一起使用顶点算子代数理论来研究Z-代数。共形场理论是描述凝聚态物理中的二维临界现象和弦理论中弦的经典运动的重要物理理论。保形场理论除了在物理学中具有重要意义外，其优美而丰富的数学结构也引起了许多数学家的兴趣。在共形场理论的研究中，揭示了无穷维李代数和群的表示、Riemann曲面和代数曲线、Monster零星群、模函数和模形式、椭圆亏格和纽结理论等数学分支之间的新关系。

9401851 Lepowsky The principal investigators will investigate vertex operator algebras and Lie algebras. One will study the new concept of vertex tensor category. The other will construct a new type of basis for the free Lie algebra and to study affinization of certain simple Lie algebras of Cartan type in prime characteristic. Together they will use vertex operator algebra theory to study Z-algebras. Conformal field theory is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory also has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera, and knot theory, is revealed in the study of conformal field theory.