On a question of D. Shlyakhtenko

Chifan, Ionut; Ioana, Adrian

doi:10.1090/S0002-9939-2010-10553-1

On a question of D. Shlyakhtenko
HTML articles powered by AMS MathViewer

by Ionut Chifan and Adrian Ioana PDF

Proc. Amer. Math. Soc. 139 (2011), 1091-1093 Request permission

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.

References

H. A. Dye, On groups of measure preserving transformations. II, Amer. J. Math. 85 (1963), 551–576. MR 158048, DOI 10.2307/2373108
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, DOI 10.1017/S0143385705000258
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, DOI 10.1090/S0273-0979-1980-14702-3
Narutaka Ozawa, Amenable actions and applications, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1563–1580. MR 2275659
Narutaka Ozawa, A Kurosh-type theorem for type $\rm II_1$ factors, Int. Math. Res. Not. , posted on (2006), Art. ID 97560, 21. MR 2211141, DOI 10.1155/IMRN/2006/97560
Sorin Popa, Orthogonal pairs of $\ast$-subalgebras in finite von Neumann algebras, J. Operator Theory 9 (1983), no. 2, 253–268. MR 703810
Sorin Popa, Strong rigidity of $\rm II_1$ factors arising from malleable actions of $w$-rigid groups. I, Invent. Math. 165 (2006), no. 2, 369–408. MR 2231961, DOI 10.1007/s00222-006-0501-4
S. Popa, Revisiting some problems in $W^{*}$-rigidity, 2009. Available at http://www.math. ucla.edu/~popa/tamu0809rev.pdf