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arXiv · 2310.20594

Tracially Complete C*-Algebras

José R. Carrión·Jorge Castillejos·Samuel Evington·James Gabe·Christopher Schafhauser·Aaron Tikuisis·Stuart White
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Abstract

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.

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José R. Carrión, Jorge Castillejos, Samuel Evington, James Gabe, Christopher Schafhauser, Aaron Tikuisis, Stuart White. 2023-10-31. Tracially Complete C*-Algebras. https://arxiv.org/abs/2310.20594

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