Derivations, quantum Dirichlet forms, and deformation/rigidity theory in von Neumann algebras

冯诺依曼代数中的导数、量子狄利克雷形式和变形/刚性理论

• 批准号: 0901510
• 负责人: Jesse Peterson
• 金额: $ 12.43万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-15 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901510&HistoricalAwards=false
• 关键词: Derivations; quantum; Dirichlet; forms; deformation

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The theory of von Neumann algebras is a non-commutative integration theory which was first developed by F. Murray and J. von Neumann as a tool for understanding representation theory for groups as well as providing a mathematical framework for quantum mechanics. Recently the appearance of new rigidity phenomena in von Neumann algebras has led to deeper understanding and to the solutions to many longstanding problems both in von Neumann algebras and in other areas such as orbit equivalence ergodic theory and measurable equivalence relations. There has also emerged recently a connection between deformation/rigidity theory, free probability, group cohomology, and derivations/quantum Dirichlet forms on von Neumann algebras. It is the intent of this author to investigate these new connections in order to gain more understanding of the relationship which is developing, and to use this understanding in order to approach some deep problems from new perspectives.

该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。冯·诺伊曼（Von Neumann）代数的理论是一种非共同的整合理论，该理论最初是由F. Murray和J. von Neumann开发的，是理解群体代表理论的工具，并为量子力学提供了数学框架。最近，冯·诺伊曼（Von Neumann）代数中新的刚性现象的出现导致了更深入的理解，并在冯·诺伊曼（Von Neumann）代数以及其他领域（例如轨道等效性麦角理论和可测量的等效关系）中解决了许多长期存在的问题的解决方案。最近，在von Neumann代数上形成了变形/刚性理论，自由概率，群体的共同论和衍生/量子迪里奇的形式之间，也出现了联系。作者的目的是调查这些新的联系，以便对正在发展的关系有更多的了解，并使用这种理解，以便从新的角度解决一些深层问题。