On a question of D. Shlyakhtenko
Authors:
Ionut Chifan and Adrian Ioana
Journal:
Proc. Amer. Math. Soc. 139 (2011), 10911093
MSC (2010):
Primary 46L10; Secondary 37A20
Published electronically:
August 23, 2010
MathSciNet review:
2745659
Fulltext PDF
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 measurepreserving 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
(28 #1275)
 [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
(2006i:22024), 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
(80j:28031), 10.1090/S027309791980147023
 [4]
Narutaka
Ozawa, Amenable actions and applications, International
Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006,
pp. 1563–1580. MR 2275659
(2008k:46185)
 [5]
Narutaka
Ozawa, A Kuroshtype theorem for type 𝐼𝐼₁
factors, Int. Math. Res. Not. , posted on (2006), Art. ID 97560, 21.
MR
2211141 (2006m:46078), 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
(84h:46077)
 [7]
Sorin
Popa, Strong rigidity of 𝐼𝐼₁ factors arising
from malleable actions of 𝑤rigid groups. I, Invent. Math.
165 (2006), no. 2, 369–408. MR 2231961
(2007f:46058), 10.1007/s0022200605014
 [8]
S. Popa, Revisiting some problems in rigidity, 2009. Available at http://www.math. ucla.edu/~popa/tamu0809rev.pdf
 [1]
 H.A. Dye, On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551576. MR 0158048 (28:1275)
 [2]
 D. Gaboriau, Examples of groups that are measure equivalent to the free group, Ergodic Theory and Dynam. Systems 25(6) (2005), 18091827. MR 2183295 (2006i:22024)
 [3]
 D. Ornstein and B. Weiss, Ergodic theory of the amenable groups. I. The Rokhlin Lemma, Bull. Amer. Math. Soc. (N.S.) 2 (1980), 161164. MR 551753 (80j:28031)
 [4]
 N. Ozawa, Amenable actions and applications, International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 15631580. MR 2275659 (2008k:46185)
 [5]
 N. Ozawa, A Kuroshtype theorem for type factors, Int. Math. Res. Not. (2006), Art. ID 97560, 21 pp. MR 2211141 (2006m:46078)
 [6]
 S. Popa, Orthogonal pairs of subalgebras in finite von Neumann algebras, J. Operator Theory 9(2) (1983), 253268. MR 703810 (84h:46077)
 [7]
 S. Popa, Strong rigidity for factors arising from malleable actions of wrigid groups. I, Invent. Math. 165(2) (2006), 369408. MR 2231961 (2007f:46058)
 [8]
 S. Popa, Revisiting some problems in rigidity, 2009. Available at http://www.math. ucla.edu/~popa/tamu0809rev.pdf
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2010):
46L10,
37A20
Retrieve articles in all journals
with MSC (2010):
46L10,
37A20
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:
http://dx.doi.org/10.1090/S000299392010105531
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.
