Bass-Serre rigidity results in von Neumann algebras

@article{Chifan2008BassSerreRR,
  title={Bass-Serre rigidity results in von Neumann algebras},
  author={Ionut Chifan and Cyril Houdayer},
  journal={arXiv: Operator Algebras},
  year={2008}
}
We obtain new Bass-Serre type rigidity results for ${\rm II_1}$ equivalence relations and their von Neumann algebras, coming from free ergodic actions of free products of groups on the standard probability space. As an application, we show that any non-amenable factor arising as an amalgamated free product of von Neumann algebras $\mathcal{M}_1 \ast_B \mathcal{M}_2$ over an abelian von Neumann algebra $B$, is prime, i.e. cannot be written as a tensor product of diffuse factors. This gives, both… 
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