Nuclear dimension for an inclusion of unital C*-algebras

Abstract

Let $P\subset A$ be an inclusion of separable unital C*-algebras with finite Watatani index. Suppose that $E:A\to P$ has the Rokhlin property, that is, there is a projection $e\in A^{\prime }\cap A^{\infty }$ such that $E^{\infty }(e)=(\mathrm{Index}E{)}^{-1}1$. We show that if $A$ has nuclear dimension $n$, then $P$ has nuclear dimension less than or equal to $n$. In particular, if an action $\alpha$ of a finite group $G$ on $A$ has the Rokhlin property, then the nuclear dimension of the crossed product algebra $A{⋊}_{\alpha }G$ is less than or equal to that of $A$.

16 pages

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Cited by in corpus (2)

• The Jiang-Su absorption for inclusions of unital C*-algebras
• Rokhlin Property for Group Actions on Hilbert $C^{\ast }$-modules