A unified approach for classifying simple nuclear C*-algebras

Ben Bouwen (University of Southern Denmark)

Thursday 31st October 16:00-17:00 Maths 311B

Abstract

The classification program of C*-algebras aims to classify simple, separable, nuclear C*-algebras by their K-theory and traces, inspired by analogous results obtained for von Neumann algebras. A landmark result in this project was obtained in 2015, building upon the work of numerous researchers over the preceding 20 years. More recently, Carrión, Gabe, Schafhauser, Tikuisis and White developed a new, more abstract approach to classification, which connects more explicitly to the von Neumann algebraic classification results. In their paper, they carry out this approach in the stably finite setting, while for the purely infinite case, they refer to the original result obtained by Kirchberg and Phillips. In this talk, I provide an overview of how the new approach can be adapted to classify purely infinite C*-algebras, recovering the Kirchberg-Phillips classification by K-theory and obtaining Kirchberg's absorption theorems as corollaries of classification rather than (pivotal) ingredients. This is joint work with Jamie Gabe.

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