Remarks on the diagonal embedding and strong 1-boundedness. (English) Zbl 1536.46050
Summary: We identify a large class of hyperbolic groups whose von Neumann algebras are not strongly 1-bounded: Sela’s hyperbolic towers over \(F_2\) subgroups. We also show that any intermediate subalgebra of the diagonal embedding of \(L(F_2)\) into its ultrapower does not have Property (T).
MSC:
| 46L10 | General theory of von Neumann algebras |
| 20A15 | Applications of logic to group theory |
| 20F67 | Hyperbolic groups and nonpositively curved groups |
| 22D55 | Kazhdan’s property (T), the Haagerup property, and generalizations |
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