PreprintCC BY 4.0arXiv
The hyperfinite II_1 factor is not quasidiagonal
Abstract
We construct an MF C*-algebra A such that the spatial tensor product of A and the hyperfinite II_1 factor R contains a proper isometry. Consequently, stable finiteness of C*-algebras is not stable under tensor product and the hyperfinite II_1 factor is not a quasidiagonal C*-algebra. The C*-algebra A is non-simple and has only non-faithful tracial states. This result was obtained using OpenAI's Chat GPT Pro 6.0.
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BibTeX
@misc{ozawa2026hyperfinite,
title = {{The hyperfinite II_1 factor is not quasidiagonal}},
author = {Narutaka Ozawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08892},
eprint = {2609.08892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The hyperfinite II_1 factor is not quasidiagonal
AU - Narutaka Ozawa
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08892
UR - https://arxiv.org/abs/2609.08892
AB - We construct an MF C*-algebra A such that the spatial tensor product of A and the hyperfinite II_1 factor R contains a proper isometry. Consequently, stable finiteness of C*-algebras is not stable under tensor product and the hyperfinite II_1 factor is not a quasidiagonal C*-algebra. The C*-algebra A is non-simple and has only non-faithful tracial states. This result was obtained using OpenAI's Chat GPT Pro 6.0.
ER -