KK-rigidity of simple nuclear C*-algebras

Christopher Schafhauser
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Abstract

It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras which either have real rank zero or unique trace are isomorphic if and only if they are homotopy equivalent. It is further shown that two finite strongly self-absorbing C$^*$-algebras are isomorphic if and only if they are $KK$-equivalent in a unit-preserving way.
简单核 C* 结构的 KK 刚性
研究表明,如果 $A$ 和 $B$ 是单原子可分离简单核 $\mathcalZ$ 稳定 C$^*$ 对象,并且存在一个在 $K$ 理论和迹线上可反转的单原子嵌入 $A \rightarrow B$,那么 $A \cong B$。具体地说,当且仅当两个同调等价的可分离简单核 $mathcal Z$ 稳定 C$^*$ 对象的实阶为零或迹线唯一时,它们是同构的。研究进一步证明,当且仅当两个有限强自吸收 C$^*$ 对象以单位保留的方式等价于 $KK$ 时,它们是同构的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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