A non co-hyperlinear IRS exists on any non-abelian free group, yielding via simplified reduction an equivalence relation whose von Neumann algebra is not Connes embeddable.
[BO] Nathanial Patrick Brown and Narutaka Ozawa
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There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable
A non co-hyperlinear IRS exists on any non-abelian free group, yielding via simplified reduction an equivalence relation whose von Neumann algebra is not Connes embeddable.