Bass-Serre rigidity results in von Neumann algebras

Details Bass-Serre rigidity results in von Neumann algebras Bass-Serre rigidity results in von Neumann algebras

2008-05-11

arxiv.org/abs/0805.1566v5

Duke Math. J. 153 (2010), 23-54.

Mathematics

Operator Algebras

27 pages.

Scientific paper

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 in the type ${\rm II_1}$ and in the type ${\rm III}$ case, new examples of prime factors.

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