On Popa’s factorial commutant embedding problem

Goldbring, Isaac

doi:10.1090/proc/15141

On Popa’s factorial commutant embedding problem
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Proc. Amer. Math. Soc. 148 (2020), 5007-5012 Request permission

Abstract:

An open question of Sorin Popa asks whether or not every $\mathcal {R}^{\mathcal {U}}$-embeddable factor admits an embedding into $\mathcal {R}^{\mathcal {U}}$ with factorial relative commutant. We show that there is a locally universal McDuff II$_1$ factor $M$ such that every property (T) factor admits an embedding into $M^{\mathcal {U}}$ with factorial relative commutant. We also discuss how our strategy could be used to settle Popa’s question for property (T) factors if a certain open question in the model theory of operator algebras has a positive solution.

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