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arXiv · 1608.05847

Centrally Large Subalgebras and Tracial ${\mathcal{Z}}$-Absorption

Dawn Archey·Julian Buck·N. Christopher Phillips
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Abstract

Let $A$ be a simple infinite dimensional stably finite unital C*-algebra, and let $B$ be a centrally large subalgebra of $A$. We prove that if $A$ is tracially ${\mathcal{Z}}$-absorbing if and only if $B$ is tracially ${\mathcal{Z}}$-absorbing. If $A$ and $B$ are also separable and nuclear, we prove that $A$ is ${\mathcal{Z}}$-absorbing if and only if $B$ is ${\mathcal{Z}}$-absorbing.

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Dawn Archey, Julian Buck, N. Christopher Phillips. 2016-08-20. Centrally Large Subalgebras and Tracial ${\mathcal{Z}}$-Absorption. https://arxiv.org/abs/1608.05847

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