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- W4291237265 abstract "We undertake a systematic study of W $$^*$$ -rigidity paradigms for the embeddability relation $$hookrightarrow $$ between separable $$hbox {II}_1$$ factors and its stable version $$hookrightarrow _{text {s}}$$ , obtaining large families of non stably isomorphic $$hbox {II}_1$$ factors that are mutually embeddable and families of $$hbox {II}_1$$ factors that are mutually non stably embeddable. We provide an augmentation functor $$G mapsto H_G$$ from the category of groups into icc groups, so that $$L(H_{G_1}) hookrightarrow _{text {s}}L(H_{G_2})$$ iff $$G_1 hookrightarrow G_2$$ . We construct complete intervals of $$hbox {II}_1$$ factors, including a strict chain of $$hbox {II}_1$$ factors $$(M_k)_{kin mathbb {Z}}$$ with the property that if N is any $$hbox {II}_1$$ factor with $$M_ihookrightarrow _{text {s}}N$$ and $$Nhookrightarrow _{text {s}}M_{j}$$ , then $$N cong M_k^t$$ for some $$i le k le j$$ and $$t > 0$$ ." @default.
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- W4291237265 date "2022-08-13" @default.
- W4291237265 modified "2023-10-18" @default.
- W4291237265 title "W$$^*$$-Rigidity Paradigms for Embeddings of $$hbox {II}_1$$ Factors" @default.
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- W4291237265 doi "https://doi.org/10.1007/s00220-022-04446-2" @default.
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