Duke Mathematical Journal

Bass-Serre rigidity results in von Neumann algebras

Ionut Chifan and Cyril Houdayer

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We obtain new Bass-Serre-type rigidity results for II1 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 nonamenable factor arising as an amalgamated free product of von Neumann algebras M1*BM2 over an abelian von Neumann algebra B is prime, that is, cannot be written as a tensor product of diffuse factors. This gives, both in the type II1 and in the type III cases, new examples of prime factors.

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Duke Math. J., Volume 153, Number 1 (2010), 23-54.

First available in Project Euclid: 28 April 2010

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Zentralblatt MATH identifier

Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L54: Free probability and free operator algebras 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]


Chifan, Ionut; Houdayer, Cyril. Bass-Serre rigidity results in von Neumann algebras. Duke Math. J. 153 (2010), no. 1, 23--54. doi:10.1215/00127094-2010-020. https://projecteuclid.org/euclid.dmj/1272480931

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