Mathematical Sciences: Endomorphisms of von Nuemann Algebras

数学科学：冯·诺伊曼代数的自同态

• 批准号: 9401464
• 负责人: Robert Powers
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401464&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Endomorphisms; von; Nuemann

9401464 Powers Powers proposes to study continuous one parameter semigroups of star endomorphisms of operator algebras. Particular emphasis will be given to the simplest case of the full algebra of operators on Hilbert space and binary shifts on hyperfinite factors of type II_1. Pimsner will continue the investigation of Kasparov's bivariant K-functor in its equivariant form, especially in its applications to the study of C*-algebras and groups and their actions on different kinds of spaces. Investigations will also be made of the related study of Hilbert bimodules and their connection to both KK-theory and to the theory of subfactors. Operators can be considered as infinite generalizations of matrices. Given their natural addition and multiplication, a collection of operators can be considered as an operator algebra. A subalgebra of certain types of operator algebras is called a subfactor. The relations between subfactors has remarkable connection with geometry and mathematical physics. The work of Pimsner will contribute to the connections. Powers will study actions on operator algebras. These actions are related to important questions in the theory of subfactors mentioned above. ***

9401464次方提出研究算子代数的星自同态的连续单参数半群。Pimsner将继续研究等变形式的Kasparov双变K-函子，特别是它在研究C*-代数和群及其在不同类型空间上的作用方面的应用。此外，还将对Hilbert双模的相关研究以及它们与KK-理论和子因子理论的联系进行研究。算子可以看作是矩阵的无限推广。给定它们的自然加法和乘法，运算符的集合可以被认为是一个运算符代数。某些类型的算子代数的子代数称为子因子。子因素之间的关系与几何和数学物理有着显著的联系。皮姆斯纳的工作将有助于建立联系。POWERS将研究算子代数上的作用。这些行为与上述亚因素理论中的重要问题有关。***