A unified approach for classifying simple nuclear $C^\ast$-algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910756435394560 |
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| author | Bouwen, Ben Gabe, James |
| author_facet | Bouwen, Ben Gabe, James |
| contents | We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carrión--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital nuclear stably finite $\mathcal Z$-stable $C^\ast$-algebras satisfying the UCT. Not only does this give a unified approach to classifying stably finite and purely infinite $C^\ast$-algebras, in contrast to the other proofs of the Kirchberg--Phillips theorem, our proof does not rely on Kirchberg's Geneva Theorems, but instead implies them as corollaries (for nuclear $C^\ast$-algebras). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unified approach for classifying simple nuclear $C^\ast$-algebras Bouwen, Ben Gabe, James Operator Algebras 46L35 We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carrión--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital nuclear stably finite $\mathcal Z$-stable $C^\ast$-algebras satisfying the UCT. Not only does this give a unified approach to classifying stably finite and purely infinite $C^\ast$-algebras, in contrast to the other proofs of the Kirchberg--Phillips theorem, our proof does not rely on Kirchberg's Geneva Theorems, but instead implies them as corollaries (for nuclear $C^\ast$-algebras). |
| title | A unified approach for classifying simple nuclear $C^\ast$-algebras |
| topic | Operator Algebras 46L35 |
| url | https://arxiv.org/abs/2412.15968 |