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arXiv · 1802.06628

A remark on the ultrapower algebra of the hyperfinite factor

Ionut Chifan·Sayan Das
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Abstract

On page 43 in \cite{Po83} Sorin Popa asked whether the following property holds: \emph{If $\omega$ is a free ultrafilter on $\mathbb N$ and $\mathcal R_1\subseteq \mathcal R$ is an irreducible inclusion of hyperfinite II$_1$ factors such that $\mathcal R'\cap \mathcal R^\omega\subseteq \mathcal R^\omega_1$ does it follows that $\mathcal R_1=\mathcal R$?} In this short note we provide an affirmative answer to this question.

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Ionut Chifan, Sayan Das. 2018-02-19. A remark on the ultrapower algebra of the hyperfinite factor. https://arxiv.org/abs/1802.06628

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