Similarity degree of a class of C^*-algebras

2014/07/05 by Qian, Wenhua, Shen, Junhao
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1407.1348

Abstract

Suppose that \mathcal M is a countably decomposable type II₁ von Neumann algebra and \mathcal A is a separable, non-nuclear, unital C^*-algebra. We show that, if \mathcal M has Property Γ, then the similarity degree of \mathcal M is less than or equal to 5. If \mathcal A has Property c^*-Γ, 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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