KK-rigidity of simple nuclear C*-algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916384249741312 |
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| author | Schafhauser, Christopher |
| author_facet | Schafhauser, Christopher |
| contents | It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras which either have real rank zero or unique trace are isomorphic if and only if they are homotopy equivalent. It is further shown that two finite strongly self-absorbing C$^*$-algebras are isomorphic if and only if they are $KK$-equivalent in a unit-preserving way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KK-rigidity of simple nuclear C*-algebras Schafhauser, Christopher Operator Algebras It is shown that if $A$ and $B$ are unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras and there is a unital embedding $A \rightarrow B$ which is invertible on $KK$-theory and traces, then $A \cong B$. In particular, two unital separable simple nuclear $\mathcal Z$-stable C$^*$-algebras which either have real rank zero or unique trace are isomorphic if and only if they are homotopy equivalent. It is further shown that two finite strongly self-absorbing C$^*$-algebras are isomorphic if and only if they are $KK$-equivalent in a unit-preserving way. |
| title | KK-rigidity of simple nuclear C*-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2408.02745 |