Some results on tracial stability and graph products
Abstract
We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a selective version of Lin's Theorem for almost commuting operators. The second application addresses some approximation properties of right-angled Artin groups. In particular, we show that the full C*-algebra of any right-angled Artin group is quasidiagonal and thus has a non-trivial amenable trace, and then we apply tracial stability to show when these amenable traces are in fact locally finite dimensional.
Keywords
Cite
@article{arxiv.1808.04664,
title = {Some results on tracial stability and graph products},
author = {Scott Atkinson},
journal= {arXiv preprint arXiv:1808.04664},
year = {2019}
}
Comments
Title changed (formerly titled "A selective version of Lin's Theorem"). Emphasis shifted to treat the tracial stability result on pincushion graph products as the main result with no significant change in content. 18 pages. Submitted version. Comments welcome!