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15 May 2010 Bass-Serre rigidity results in von Neumann algebras
Ionut Chifan, Cyril Houdayer
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Duke Math. J. 153(1): 23-54 (15 May 2010). DOI: 10.1215/00127094-2010-020

Abstract

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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Ionut Chifan. Cyril Houdayer. "Bass-Serre rigidity results in von Neumann algebras." Duke Math. J. 153 (1) 23 - 54, 15 May 2010. https://doi.org/10.1215/00127094-2010-020

Information

Published: 15 May 2010
First available in Project Euclid: 28 April 2010

zbMATH: 1201.46057
MathSciNet: MR2641939
Digital Object Identifier: 10.1215/00127094-2010-020

Subjects:
Primary: 46L10
Secondary: 46L54, 46L55

Rights: Copyright © 2010 Duke University Press

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Vol.153 • No. 1 • 15 May 2010
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