Non-embeddable II 1 _1 1 ​ factors resembling the hyperfinite II 1 _1 1 ​ factor

[摘要] We consider various statements that characterize the hyperfinite II1_11​ factors amongst embeddable II1_11​ factors in the non-embeddable situation. In particular, we show that “generically” a II1_11​ factor has the Jung property (which states that every embedding of itself into its ultrapower is unitarily conjugate to the diagonal embedding) if and only if it is self-tracially stable (which says that every such embedding has an approximate lifting). We prove that the enforceable factor, should it exist, has these equivalent properties. Our techniques are model-theoretic in nature. We also show how these techniques can be used to give new proofs that the hyperfinite II1 factor has the aforementioned properties.

[学科分类] 神经科学

[关键词] Connes embedding problem;enforceable II factor;Jung property for II factors