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

Journal of noncommutative geometry

article

Guihua Gong¹  Huaxin Lin³  Zhuang Niu⁵ 

[1] Hebei Normal University;University of Puerto Rico;East China Normal University;University of Oregon;University of Woyming

关键词: Homomorphisms;    simpleC -algebras;   

DOI  :  10.4171/jncg/490

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

Let AAA and BBB be unital finite separable simple amenable C∗C^*C∗-algebras which satisfy the UCT, and BBB is Z\mathcal{Z}Z-stable. Following Gong, Lin, and Niu (2020), we show that two unital homomorphisms from AAA to BBB are approximately unitarily equivalent if and only if they induce the same element in KL(A,B)KL(A,B)KL(A,B), the same affine map on tracial states, and the same Hausdorffified algebraic K1K_1K1​ group homomorphism. A complete description of the range of the invariant for unital homomorphisms is also given.

【 授权许可】

CC BY