| Abstract |
Let $A$ and $B$ be unital finite separable simple amenable $C^\*$-algebras which satisfy the UCT, and $B$ is $\mathcal{Z}$-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 $KL(A,B)$, 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. |
| Authors |
Guihua Gong , Huaxin Lin , Zhuang Niu 
|
| Journal Info |
European Mathematical Society | Journal of Noncommutative Geometry , vol: 17
, iss: 3
, pages: 835 - 898
|
| Publication Date |
7/14/2023 |
| ISSN |
1661-6952 |
Type |
article |
| Open Access |
gold
|
| DOI |
https://doi.org/10.4171/jncg/490 |
| Keywords |
Homology (Score: 0.541553) , Homological Dimensions (Score: 0.507834) , Cohomology (Score: 0.507093)
|
