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The ultrapower ℛω is not a group factor
Abstract
Let (ℳn)ngeqslant 1 be a sequence of type II1 factors with property Γ and let ω be a free ultrafilter on ℕ. We prove that every subfactor of the ultraproduct ∏ωℳn of finite Jones index is not isomorphic to the group von Neumann algebra of any discrete group. In particular, the ultrapower ℛω of the hyperfinite type II1 factor ℛ is not a group factor.
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BibTeX
@misc{ma2026ultrapower,
title = {{The ultrapower $\mathcal R^ω$ is not a group factor}},
author = {Minghui Ma},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04926},
eprint = {2611.04926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04926},
}
RIS
TY - UNPB
TI - The ultrapower ℛ^ω is not a group factor
AU - Minghui Ma
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04926
UR - https://arxiv.org/abs/2611.04926
AB - Let (ℳ_n)_ngeqslant 1 be a sequence of type II_1 factors with property Γ and let ω be a free ultrafilter on ℕ. We prove that every subfactor of the ultraproduct ∏_ωℳ_n of finite Jones index is not isomorphic to the group von Neumann algebra of any discrete group. In particular, the ultrapower ℛ^ω of the hyperfinite type II_1 factor ℛ is not a group factor.
ER -