单$\mathcal{Z}$ -稳定$C^{*}$ -代数的自同构群
The Automorphism group of a simple $\mathcal{Z}$-stable $C^{*}$-algebra
摘要：
研究了有单位元的单$\mathcal{Z}$ -稳定$C^{*}$ -代数的自同构群.本文将作者在\cite{pr_auto}中的结果推广到$\mathcal{Z}$ -稳定的$C^{*}$ -代数$\mathfrak{A}$，使得$\mathfrak{A} \otimes \mathfrak{B}$是一个可分的、核的、单的、迹AI代数，满足Rosenberg和Schochet的泛系数定理（UCT）\cite{uct} .利用Lin在\cite{hl_asyunit}和Winter在\cite{ww_localelliott}中的结果，利用$K$ -理论和迹对满足上述条件的$C^{\ast}$ -代数进行了分类.
英文摘要：
We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that $\mathfrak{A} \otimes \mathfrak{B}$ is a separable, nuclear, simple, tracially AI algebras satisfying the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet \cite{uct}. By the results of Lin in \cite{hl_asyunit} and Winter in \cite{ww_localelliott}, $C^{\ast}$-algebras that satisfies the above condition are classified via $K$-theory and traces.
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