The Automorphism group of a simple $\mathcal{Z}$-stable $C^{*}$-algebra

Details The Automorphism group of a simple $\mathcal{Z}$-stable $C^{*}$-algebra The Automorphism group of a simple $\mathcal{Z}$-stable $C^{*}$-algebra

2010-03-11

arxiv.org/abs/1003.2404v3

Mathematics

Operator Algebras

Improved the exposition of Section 3 and Section 4, added other references

Scientific paper

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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