From actions to operator algebras and their equilibrium states

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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.