Simple graph algebras

Becky Armstrong (University of Sydney)

Thursday 13th September, 2018 16:00-17:00 Maths 311B


Since their introduction twenty years ago, C*-algebras associated to directed graphs have become a popular tool for investigating various classes of C*-algebras, because analytical properties of these C*-algebras depend on much simpler combinatorial properties of the underlying graphs. One such analytical property is simplicity, which plays a fundamental role in the classification program for C*-algebras. In this talk I will first recall the characterisation of simplicity for directed graph C*-algebras. I will then describe the results of my PhD research, in which I characterise simplicity of twisted C*-algebras of topological higher-rank graphs in terms of the underlying graphical and cohomological data. These C*-algebras are constructed using groupoid techniques for the purpose of this simplicity characterisation, but I will also briefly describe two product-system models for twisted C*-algebras of topological higher-rank graphs. (This is joint work with my PhD supervisors, Nathan Brownlowe and Aidan Sims.)

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