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

[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.

[学科分类] 神经科学

[关键词] Homomorphisms;simpleC -algebras