On invariant von Neumann subalgebras rigidity property

We say that a countable discrete group Gamma satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every Gamma-invariant von Neumann subalgebra M in L(Gamma) is of the form L(Lambda) for some normal subgroup Lambda d Gamma. We show many "negatively curved" groups, including all torsion free non -amenable hyperbolic groups and torsion free groups with positive first L2-Betti number under a mild assumption, and certain finite direct product of them have this property. We also discuss whether the torsion-free assumption can be relaxed.(c) 2022 Elsevier Inc. All rights reserved.