Tracially Complete C*-Algebras
| Autor: | Carrión, José R., Castillejos, Jorge, Evington, Samuel, Gabe, James, Schafhauser, Christopher, Tikuisis, Aaron, White, Stuart |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 138 pages; edits to made to results 6.3, 6.4, 6.15 and 6.16 |
| Databáze: | arXiv |
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