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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a question of D. Shlyakhtenko


Authors: Ionut Chifan and Adrian Ioana
Journal: Proc. Amer. Math. Soc. 139 (2011), 1091-1093
MSC (2010): Primary 46L10; Secondary 37A20
Published electronically: August 23, 2010
MathSciNet review: 2745659
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Abstract: In this short paper we construct two countable, infinite conjugacy class (ICC) groups which admit free, ergodic, probability measure-preserving orbit equivalent actions but whose group von Neumann algebras are not (stably) isomorphic.


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Ionut Chifan
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
Email: ionut.chifan@vanderbilt.edu

Adrian Ioana
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095 – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
Email: aioana@caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10553-1
PII: S 0002-9939(2010)10553-1
Keywords: von Neumann algebra, $W^{*}$-equivalence, orbit equivalence
Received by editor(s): September 3, 2009
Received by editor(s) in revised form: April 5, 2010
Published electronically: August 23, 2010
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.