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Department of Mathematics,
University of California San Diego

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Math 243 - Functional Analysis Seminar

Scott Atkinson

Vanderbilt University

Tracial stability and graph products

Abstract:

A unital $C^\ast$-algebra $A$ is tracially stable if maps on $A$ that are approximately (in trace) unital $\ast$-homomorphisms can be approximated (in trace) by honest unital $\ast$-homomorphisms on $A$. Tracial stability is closed under free products and tensor products with abelian $C^\ast$-algebras. In this talk we expand these results to show that for a graph from a certain class, the corresponding graph product (a simultaneous generalization of free and tensor products) of abelian $C^\ast$-algebras is tracially stable. We will then discuss two applications of this result: a selective version of Lin’s Theorem and a characterization of the amenable traces on certain right-angled Artin groups.

Host: Adrian Ioana

November 13, 2018

10:00 AM

AP&M 6402

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