Conference Support - - Second East Coast Operator Algebras Symposium (ECOAS); October 2-3, 2004; Annapolis, MD

会议支持 - 第二届东海岸算子代数研讨会（ECOAS）；

• 批准号: 0416387
• 负责人: Geoffrey Price
• 金额: $ 2.15万
• 依托单位: United States Naval Academy
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0416387&HistoricalAwards=false
• 关键词: Conference; Support; Second; East; Coast

AbstractPrice This proposal is directed towards the investigation of some problems on dynamical systems on von Neumann algebras, and is related to recent work by a number of authors on the subject of semigroups of endomorphisms on von Neumann algebra factors. This research project involves a number of areas of mathematics, including operator algebras, finite fields, number theory, and combinatorics. In contrast to semigroups of automorphisms, a semigroup of endomorphisms may be viewed as a dynamical system that may proceed forward but not backward in time. It is remarkable how challenging this subject has proven to be in light of the relatively simpler theory of one-parameter semigroups of automorphisms on a type I factor. A principal goal of this proposal is to make additional progress in the classification of one-parameter semigroups of unital endomorphisms, analogous to Wigner's characterization of groups of automorphisms acting on factors of type I. The study of operator algebras traces its origins back to the work of von Neumann and others. Their goal was to construct mathematical models that capture the behavior of quantum mechanical systems, and to use these models to make predictions about the time evolution of such systems. As knowledge has grown and techniques in the field have been refined, connections have been established between operator algebras and a number of other areas of mathematics and science. This proposal involves connections among the fields of operator algebras, commutative algebra, number theory, and combinatorics. The principal objects of study in this project are known as binary shifts on a certain type of operator algebra and are defined using bitstreams of 0's and 1's such as one studies in the theory of linear recurring sequences. A major goal of this project is to complete the classification of the binary shifts and to relate this classification to the analysis of linear recurring sequences. Binary shifts will also be studied for their potential applications to the theory of quantum dynamical systems, specifically those systems that may proceed forward, but not backward, in time.

AbstractPrice 该提案旨在研究冯·诺依曼代数动力系统的一些问题，并与许多作者最近关于冯·诺依曼代数因子自同态半群的工作相关。 该研究项目涉及多个数学领域，包括算子代数、有限域、数论和组合学。 与自同态半群相反，自同态半群可以被视为可以在时间上向前但不能向后移动的动力系统。 值得注意的是，鉴于 I 型因子的单参数自同构半群的相对简单的理论，这一主题被证明是多么具有挑战性。 该提案的主要目标是在单位自同态的单参数半群的分类方面取得额外进展，类似于维格纳对作用于 I 型因子的自同构群的表征。算子代数的研究可以追溯到其工作冯·诺依曼等人。 他们的目标是构建捕捉量子力学系统行为的数学模型，并使用这些模型来预测此类系统的时间演化。 随着该领域知识的增长和技术的完善，算子代数与数学和科学的许多其他领域之间已经建立了联系。 该提案涉及算子代数、交换代数、数论和组合学领域之间的联系。 该项目的主要研究对象被称为某种类型的算子代数上的二进制移位，并使用 0 和 1 的比特流来定义，例如线性循环序列理论中的一项研究。 该项目的主要目标是完成二元移位的分类，并将该分类与线性循环序列的分析联系起来。 还将研究二元平移在量子动力系统理论中的潜在应用，特别是那些可能在时间上向前但不能向后移动的系统。