Homomorphisms into simple $\mathcal{Z}$-stable $C^*$-algebras, II

Guihua Gong; Huaxin Lin; Zhuang Niu

doi:10.4171/jncg/490

JournalsjncgVol. 17, No. 3pp. 835–898

Homomorphisms into simple $Z$ -stable $C^{*}$ -algebras, II

Guihua Gong
Hebei Normal University, China; University of Puerto Rico, Rio Piedras, USA
Huaxin Lin
East China Normal University, Shanghai, China; University of Oregon, Eugene, USA
Zhuang Niu
University of Woyming, Laramie, USA

$Homomorphisms into simple $\mathcal{Z}$-stable $C^*$-algebras, II cover$

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Abstract

Let $A$ and $B$ be unital finite separable simple amenable $C^{*}$ -algebras which satisfy the UCT, and $B$ is $Z$ -stable. Following Gong, Lin, and Niu (2020), we show that two unital homomorphisms from $A$ to $B$ are approximately unitarily equivalent if and only if they induce the same element in $K L (A, B)$ , the same affine map on tracial states, and the same Hausdorffified algebraic $K_{1}$ group homomorphism. A complete description of the range of the invariant for unital homomorphisms is also given.

Cite this article

Guihua Gong, Huaxin Lin, Zhuang Niu, Homomorphisms into simple $Z$ -stable $C^{*}$ -algebras, II. J. Noncommut. Geom. 17 (2023), no. 3, pp. 835–898

DOI 10.4171/JNCG/490