The dynamical Kirchberg-Phillips theorem

Gabor Szabo (KU Leuven)

Thursday 25th November, 2021 16:00-17:00 Maths 311B


The Kirchberg-Phillips theorem was the first satisfactory instance of a truly abstract classification theorem of simple C*-algebras and hence represents a colossal milestone in the Elliott program. In a nutshell, it says that simple nuclear and purely infinite C*-algebras are classified up to isomorphism by Kasparov theory (KK-theory). In this talk I will outline (in broad strokes) the main results of ongoing work with James Gabe in which we prove a dynamical version of the Kirchberg-Phillips theorem. Given an arbitrary (second-countable) locally compact group G, we show that all amenable G-actions on Kirchberg algebras satisfying a certain outerness condition are classified, up to cocycle conjugacy, by equivariant Kasparov theory. If G is discrete, then this aforementioned outerness condition is indeed nothing but outerness in the ordinary sense. The purpose of this talk is to give an overview of our theory and the most basic relevant concepts, but there shan't be any focus on technical details or proofs.

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