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Winter 2018 Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property
Hiroyuki Osaka, Tamotsu Teruya
Adv. Oper. Theory 3(1): 123-136 (Winter 2018). DOI: 10.22034/aot.1703-1145

Abstract

Let $P \subset A$ be an inclusion of unital $C^*$-algebras and $E: A \rightarrow P$ be a faithful conditional expectation of index finite type. Suppose that $E$ has the Rokhlin property. Then $\mathrm{dr}(P) \leq \mathrm{dr}(A)$ and $dim_{nuc}(P) \leq dim_{nuc}(A)$. This can be applied to Rokhlin actions of finite groups. We also show that under the same above assumption if $A$ is exact and pure, that is, the Cuntz semigroups $W(A)$ has strict comparison and is almost divisible, then $P$ and the basic contruction $C^*\langle A, e_P \rangle$ are also pure.

Citation

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Hiroyuki Osaka. Tamotsu Teruya. "Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property." Adv. Oper. Theory 3 (1) 123 - 136, Winter 2018. https://doi.org/10.22034/aot.1703-1145

Information

Received: 28 March 2017; Accepted: 27 April 2017; Published: Winter 2018
First available in Project Euclid: 5 December 2017

zbMATH: 06804320
MathSciNet: MR3730343
Digital Object Identifier: 10.22034/aot.1703-1145

Subjects:
Primary: 46L55
Secondary: 46L35

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 1 • Winter 2018
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