Subalgebras of AF-algebras

Christopher Schafhauser (University of Waterloo)

Friday 11th May, 2018 13:00-14:00 Maths 311B


A long-standing open question, formalized by Blackadar and Kirchberg in the mid 90’s, asks for an abstract characterization of C*-subalgebras of AF-algebras. I will discuss some recent progress on this question: every separable, exact C*-algebra which satisfies the UCT and admits a faithful, amenable trace embeds into an AF-algebra. Moreover, the AF-algebra may be chosen to be simple and unital with unique trace and the embedding may be taken to be trace-preserving. Modulo the UCT, this characterizes C*-subalgebras of simple, unital AF-algebras. As an application, for any countable, discrete, amenable group G, the reduced C*-algebra of G embeds into a UHF-algebra.

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