Tracially Complete C*-Algebras
Fuente:
arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917666994782208 |
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| author | Carrión, José R. Castillejos, Jorge Evington, Samuel Gabe, James Schafhauser, Christopher Tikuisis, Aaron White, Stuart |
| author_facet | Carrión, José R. Castillejos, Jorge Evington, Samuel Gabe, James Schafhauser, Christopher Tikuisis, Aaron White, Stuart |
| contents | We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification results for amenable tracially complete C*-algebras satisfying an appropriate version of Murray and von Neumann's property gamma for II_1 factors. In a precise sense, these results fit between Connes' celebrated theorems for injective II_1 factors and the unital classification theorem for separable simple nuclear C*-algebras. The theory also underpins arguments for the known parts of the Toms-Winter conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20594 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tracially Complete C*-Algebras Carrión, José R. Castillejos, Jorge Evington, Samuel Gabe, James Schafhauser, Christopher Tikuisis, Aaron White, Stuart Operator Algebras 46L35 We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification results for amenable tracially complete C*-algebras satisfying an appropriate version of Murray and von Neumann's property gamma for II_1 factors. In a precise sense, these results fit between Connes' celebrated theorems for injective II_1 factors and the unital classification theorem for separable simple nuclear C*-algebras. The theory also underpins arguments for the known parts of the Toms-Winter conjecture. |
| title | Tracially Complete C*-Algebras |
| topic | Operator Algebras 46L35 |
| url | https://arxiv.org/abs/2310.20594 |