Vertex Operator Algebras and Monstrous Moonshine

顶点算子代数和巨大的 Moonshine

• 批准号: 9700923
• 负责人: Chongying Dong
• 金额: $ 6万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700923&HistoricalAwards=false
• 关键词: Vertex; Operator; Algebras; Monstrous; Moonshine

ABSTRACT, DONG The principal investigator will investigate vertex operator algebras and the monstrous moonshine. Relations among vertex operator algebras, orbifold theory, modular functions and elliptic cohomology will be studied. The principal investigator will determine various module categories and construct induction functor for vertex operator algebras. The Conway-Norton's generalized moonshine conjecture is expected to be established. Vertex operator algebras are symmetry algebras in conformal field theory which is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. This is a research that starts out in the field of algebra but moves beyond that to touch knot invariants, quantum groups, integrable systems, modular forms, and conformal and topological field theories. A successful study of this project will lead to new mathematical discoveries which will be important both in mathematics and physics.

摘要，主要研究者董将研究顶点算子代数和怪异的月光。将研究顶点算子代数、奥比福尔德理论、模函数和椭圆上同调之间的关系。主要研究人员将确定各种模范类并构造顶点算子代数的归纳函子。康威-诺顿的广义月光猜想有望成立。顶点算符代数是共形场理论中的对称代数，它既描述了凝聚态物理中的二维临界现象，又描述了弦理论中的弦的经典运动。这是一项始于代数领域的研究，但超越了代数领域，涉及到纽结不变量、量子群、可积系统、模形式以及共形和拓扑场论。对这个项目的成功研究将导致新的数学发现，这在数学和物理学中都将是重要的。