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arXiv · 1407.1348

Similarity degree of a class of C$^*$-algebras

Wenhua Qian·Junhao Shen
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Abstract

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of $\mathcal M$ is less than or equal to $5$. If $\mathcal A$ has Property c$^*$-$\Gamma$, then the similarity degree of $\mathcal A$ is equal to $3$. In particular, the similarity degree of a $\mathcal Z$-stable, separable, non-nuclear, unital C$^*$-algebra is equal to $3$.

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Wenhua Qian, Junhao Shen. 2014-07-05. Similarity degree of a class of C$^*$-algebras. https://arxiv.org/abs/1407.1348

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