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arXiv · 0805.1566

Bass-Serre rigidity results in von Neumann algebras

Ionut Chifan·Cyril Houdayer
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Abstract

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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BibTeXRIS

Ionut Chifan, Cyril Houdayer. 2008-05-11. Bass-Serre rigidity results in von Neumann algebras. https://doi.org/10.1215/00127094-2010-020

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