From actions to operator algebras and their equilibrium states

从行动到算子代数及其平衡状态

• 批准号: DP170101821
• 负责人: Prof Jacqui Ramagge
• 金额: $ 19.98万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170101821
• 关键词: actions; operator; algebras; their; equilibrium

This project aims to construct C*-algebras from various types of actions and analyse their equilibrium states. Operator algebras are widely used in mathematics and to describe physical systems. They are technically challenging to work with and impossible to fully classify, making detailed analysis of large classes of examples important research in the area. This project will construct C*-algebras from various actions; analyse their equilibrium states; and consider actions of semigroups and groupoids. The project expects to produce significant mathematical outcomes, and the findings will be important beyond academia, expand Australia’s knowledge base and foster Australian competitiveness.

本项目旨在从各种类型的作用构造C*-代数并分析它们的平衡状态。算子代数广泛应用于数学和描述物理系统。它们在技术上具有挑战性，并且不可能完全分类，因此对该领域重要研究的大型示例进行详细分析。这个项目将从各种动作构造C*-代数；分析它们的平衡态；并考虑半群和类群的作用。该项目预计将产生重大的数学成果，其研究结果将在学术界之外发挥重要作用，扩大澳大利亚的知识基础，促进澳大利亚的竞争力。