##### Department of Mathematics,

University of California San Diego

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### Math 243: Seminar in Functional Analysis

## Christopher Schafhauser

#### York University

## Subalgebras of AF-Algebras

##### Abstract:

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.

Host: Adrian Ioana

### October 9, 2018

### 11:00 AM

### AP&M 6402

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