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# Obstructions to $\mathcal{Z}$-Stability for Unital Simple $C^*$-Algebras

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Published:2000-12-01
Printed: Dec 2000
• Guihua Gong
• Xinhui Jiang
• Hongbing Su
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## Abstract

Let $\cZ$ be the unital simple nuclear infinite dimensional $C^*$-algebra which has the same Elliott invariant as $\bbC$, introduced in \cite{JS}. A $C^*$-algebra is called $\cZ$-stable if $A \cong A \otimes \cZ$. In this note we give some necessary conditions for a unital simple $C^*$-algebra to be $\cZ$-stable.
 Keywords: simple $C^*$-algebra, $\mathcal{Z}$-stability, weak (un)perforation in $K_0$ group, property $\Gamma$, finiteness
 MSC Classifications: 46L05 - General theory of $C^*$-algebras

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