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A REMARK ON THE TRACIAL ROKHLIN PROPERTY

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  07 March 2018

YUAN HANG ZHANG
YUAN HANG ZHANG*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, PR China email zhangyuanhang@jlu.edu.cn
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Abstract

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To explore the difficulties of classifying actions with the tracial Rokhlin property using K-theoretic data, we construct two $\mathbb{Z}_{2}$ actions $\unicode[STIX]{x1D6FC}_{1},\unicode[STIX]{x1D6FC}_{2}$ on a simple unital AF algebra $A$ such that $\unicode[STIX]{x1D6FC}_{1}$ has the tracial Rokhlin property and $\unicode[STIX]{x1D6FC}_{2}$ does not, while $(\unicode[STIX]{x1D6FC}_{1})_{\ast }=(\unicode[STIX]{x1D6FC}_{2})_{\ast }$, where $(\unicode[STIX]{x1D6FC}_{i})_{\ast }$ is the induced map by $\unicode[STIX]{x1D6FC}_{i}$ acting on $K_{0}(A)$ for $i=1,2$.

Keywords

AF algebraautomorphism of order 2real rank zerotracial Rokhlin property

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L35: Classifications of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 3 , June 2018 , pp. 492 - 498
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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