Subfactor Theory and Applications

子因素理论与应用

• 批准号: 9970677
• 负责人: Adrian Ocneanu
• 金额: $ 7.79万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970677&HistoricalAwards=false
• 关键词: Subfactor; Theory; Applications

AbstractOcneanuOcneanu will investigate three classes of problems. The first class to be investigated concern the general discrete structure behind the rigidity results of finite depth subfactors; the second class of problems concerns the introduction and use of the new technical tools for subfactors such as the maximal atlas, the generalized intermediate subfactors and the modular matrices associated to a subfactor; and the third class of problems concerns the detailed study of concrete classes of examples such as the maximal atlas of cross products by a group, the structure of connections between Coxeter graphs, and the structure of connections between affine Coxeter graphs.This research is in the area of operator algebras, which can be thought of as the infinite dimensional analogue of the algebra of n-dimensional square matrices. This subject had its origins in the early efforts to give a rigorous mathematical foundation to quantum mechanics, and there is still a rich symbiosis between the two subjects.

摘要：本文将研究三类问题。第一类要研究的是有限深度子因子刚度结果背后的一般离散结构；第二类问题涉及子因子的新技术工具的引入和使用，如极大集、广义中间子因子和与子因子相关的模矩阵；第三类问题涉及具体类例子的详细研究，如群的叉积的极大集、Coxeter图之间的连接结构、仿射Coxeter图之间的连接结构。本研究是在算子代数领域，它可以被认为是n维方阵代数的无限维模拟。这门学科的起源是早期为量子力学提供严格的数学基础的努力，这两门学科之间仍然有丰富的共生关系。