@article {
author = {Osaka, Hiroyuki and Teruya, Tamotsu},
title = {Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property},
journal = {Advances in Operator Theory},
volume = {3},
number = {1},
pages = {123-136},
year = {2018},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
doi = {10.22034/aot.1703-1145},
abstract = {Let $P \subset A$ be an inclusion of unital $C^*$-algebras and $E\colon A \rightarrow P$ be a faithful conditional expectation of index finite type. Suppose that $E$ has the Rokhlin property. Then $\dr(P) \leq \dr(A)$ 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.},
keywords = {Rokhlin property,C*-index,nuclear dimension},
url = {http://www.aot-math.org/article_45177.html},
eprint = {http://www.aot-math.org/article_45177_609d8347a1a4c02639504efeafda0dce.pdf}
}