Central Sequence Algebras of a Purely Infinite Simple $C^{*}$-algebra

http://dx.doi.org/10.4153/CJM-2004-054-0
Canad. J. Math. 56(2004), 1237-1258

  Published:2004-12-01
 Printed: Dec 2004

We are concerned with a unital separable nuclear purely infinite simple $C^{*}$-algebra\ $A$ satisfying UCT with a Rohlin flow, as a continuation of~\cite{Kismh}. Our first result (which is independent of the Rohlin flow) is to characterize when two {\em central} projections in $A$ are equivalent by a {\em central} partial isometry. Our second result shows that the K-theory of the central sequence algebra $A'\cap A^\omega$ (for an $\omega\in \beta\N\setminus\N$) and its {\em fixed point} algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in~ \cite{Kismh}.