From actions to operator algebras and their equilibrium states

本项目旨在从各种类型的作用构造C*-代数，并分析它们的平衡态。算子代数在数学和描述物理系统中有着广泛的应用。它们在技术上具有挑战性，不可能完全分类，因此对大量实例进行详细分析是该领域的重要研究。这个项目将从各种作用构造C*-代数;分析它们的平衡状态;并考虑半群和群胚的作用。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具有重要意义，扩大澳大利亚的知识基础，并促进澳大利亚的竞争力。

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.