Tracially Complete C*-Algebras
Operator Algebras
2024-05-16 v4
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.
Keywords
Cite
@article{arxiv.2310.20594,
title = {Tracially Complete C*-Algebras},
author = {José R. Carrión and Jorge Castillejos and Samuel Evington and James Gabe and Christopher Schafhauser and Aaron Tikuisis and Stuart White},
journal= {arXiv preprint arXiv:2310.20594},
year = {2024}
}
Comments
138 pages; edits to made to results 6.3, 6.4, 6.15 and 6.16