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Central Sequence Algebras of a Purely Infinite Simple C*-algebra

Published online by Cambridge University Press:  20 November 2018

Akitaka Kishimoto
Akitaka Kishimoto*
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan e-mail: kishi@math.sci.hokudai.ac.jp
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Abstract

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We are concerned with a unital separable nuclear purely infinite simple ${{C}^{*}}$-algebra $A$ satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in $A$ are equivalent by a central partial isometry. Our second result shows that the $\text{K}$-theory of the central sequence algebra ${A}'\cap {{A}^{\omega }}$ (for an $\omega \in \beta \text{N }\!\!\backslash\!\!\text{ N}$) and its 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 [12].

Keywords

46L40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 6 , 01 December 2004 , pp. 1237 - 1258
Copyright
Copyright © Canadian Mathematical Society 2004

References

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