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 | References | Similar Articles | Additional Information

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.

**[1]**H. A. Dye,*On groups of measure preserving transformations. II*, Amer. J. Math.**85**(1963), 551–576. MR**0158048****[2]**D. Gaboriau,*Examples of groups that are measure equivalent to the free group*, Ergodic Theory Dynam. Systems**25**(2005), no. 6, 1809–1827. MR**2183295**, 10.1017/S0143385705000258**[3]**Donald S. Ornstein and Benjamin Weiss,*Ergodic theory of amenable group actions. I. The Rohlin lemma*, Bull. Amer. Math. Soc. (N.S.)**2**(1980), no. 1, 161–164. MR**551753**, 10.1090/S0273-0979-1980-14702-3**[4]**Narutaka Ozawa,*Amenable actions and applications*, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1563–1580. MR**2275659****[5]**Narutaka Ozawa,*A Kurosh-type theorem for type 𝐼𝐼₁ factors*, Int. Math. Res. Not. , posted on (2006), Art. ID 97560, 21. MR**2211141**, 10.1155/IMRN/2006/97560**[6]**Sorin Popa,*Orthogonal pairs of ∗-subalgebras in finite von Neumann algebras*, J. Operator Theory**9**(1983), no. 2, 253–268. MR**703810****[7]**Sorin Popa,*Strong rigidity of 𝐼𝐼₁ factors arising from malleable actions of 𝑤-rigid groups. I*, Invent. Math.**165**(2006), no. 2, 369–408. MR**2231961**, 10.1007/s00222-006-0501-4**[8]**S. Popa,*Revisiting some problems in -rigidity*, 2009. Available at`http://www.math. ucla.edu/~popa/tamu0809rev.pdf`

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Additional Information

**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:
https://doi.org/10.1090/S0002-9939-2010-10553-1

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.