标题： 存在一个等价关系，其冯·诺依曼代数不是康尼斯可嵌入的 显示英文标题

标题： There Is An Equivalence Relation Whose von Neumann Algebra Is Not Connes Embeddable

摘要： MIP$^*$=RE [Ji+22] 被用于证明存在一个非Connes可嵌入的迹von Neumann代数。 最近，类似的想法被用于[Bow+24, BCV24]中，以给出Aldous-Lyons猜想的否定解：在任何非交换自由群上存在一个非co-sofic IRS。 我们定义了一个IRS的超线性概念，并证明在任何非交换自由群上存在一个非co-超线性IRS，这重新证明了[Bow+24, BCV24]的主要结果。 作为推论，我们证明存在一个其von Neumann代数不是Connes可嵌入的关系。 显示英文摘要

摘要： MIP$^*$=RE [Ji+22] was used to prove the existence of a non Connes embeddable tracial von Neumann algebra. Recently, similar ideas were used in [Bow+24, BCV24] to give a negative solution to the Aldous-Lyons conjecture: there is a non co-sofic IRS on any non-abelian free group. We define a notion of hyperlinearity for an IRS and show that there is a non co-hyperlinear IRS on any non-abelian free group, which reproves the main results of [Bow+24, BCV24]. As a corollary, we prove that there is a relation whose von Neumann algebra is not Connes embeddable.