There and back again: operator algebras, algebras and dynamical systems

来来回回：算子代数、代数和动力系统

• 批准号: DP200100155
• 负责人: Prof Aidan Sims
• 金额: $ 32.38万
• 依托单位: University of Wollongong
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-06-29 至 2023-09-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100155
• 关键词: There; back; again; operator; algebras

The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.

该项目的目的是发展数学，使我们能够在动力系统和代数（包括算子代数）之间来回传递信息。动力系统-随时间变化的系统-无处不在，是现代数学及其应用的核心。在数学中，对偶性允许我们将问题从一个上下文转换到另一个更容易解决的上下文，然后再将答案转换回来。预期成果包括增加对算子代数和它们所代表的动力系统之间关系的理解。好处包括加强国际合作，提高澳大利亚在纯数学，特别是算子代数方面的能力。