AG Lie-Gruppen: J. Gabe, University of Southern Denmark: Simple AF embeddability for unimodular group C*-algebras

Simple AF embeddability for unimodular group C*-algebras – Vortragender: Jamie
Gabe, University of Southern Denmark – Einladender: Kang Li

Abstract: For any locally compact group G, the left regular (unitary)
representation generates a C*-algebra of bounded operators on the Hilbert
space L^2(G). J. Rosenberg proved in the 80’s that a discrete group G is
amenable provided its induced C*-algebra forms a quasidiagonal set of
operators on L^2(G), and he conjectured that the converse also holds. The
conjecture was confirmed in 2015 by Tikuisis, White, and Winter, and using
methods of Ozawa, Rørdam, and Sato for elementary amenable groups, they showed
the stronger result that such group C*-algebras embed into a simple
approximately finite-dimensional (AF) C*-algebra. I will report on some
developments on extending this result to unimodular groups which are amenable,
type I, or (almost) connected. The proof uses a new ultrapower construction
for tracial weights, and if time permits, I will describe how these
ultrapowers work.