%0 Journal Article
%T Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Osaka, Hiroyuki
%A Teruya, Tamotsu
%D 2018
%\ 01/01/2018
%V 3
%N 1
%P 123-136
%! Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property
%K Rokhlin property
%K C*-index
%K nuclear dimension
%R 10.22034/aot.1703-1145
%X Let $P subset A$ be an inclusion of unital $C^*$-algebras and $Ecolon A rightarrow P$ 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 $C^*langle A, e_Prangle$ are also pure.
%U http://www.aot-math.org/article_45177_609d8347a1a4c02639504efeafda0dce.pdf