HNN extensions and unique group measure space decomposition of II factors

Authors:
Pierre Fima and Stefaan Vaes

Journal:
Trans. Amer. Math. Soc. **364** (2012), 2601-2617

MSC (2010):
Primary 46L36; Secondary 20E06, 28D15, 46L54

Published electronically:
January 6, 2012

MathSciNet review:
2888221

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for a fairly large family of HNN extensions , the group measure space II factor given by an arbitrary free ergodic probability measure preserving action of has a unique group measure space Cartan subalgebra up to unitary conjugacy. From this we deduce new examples of W-superrigid group actions, i.e. where the II factor entirely remembers the group action from which it was constructed.

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Additional Information

**Pierre Fima**

Affiliation:
Department of Mathematics, K. U. Leuven, Celestijnenlaan 200B, B–3001 Leuven, Belgium

Address at time of publication:
Institute of Mathematics of Jussieu, University Denis Diderot Paris 7, 175, rue du Chevaleret, F-75013 Paris, France

Email:
pierre.fima@wis.kuleuven.be, pfima@math.jussieu.fr

**Stefaan Vaes**

Affiliation:
Department of Mathematics, K. U. Leuven, Celestijnenlaan 200B, B–3001 Leuven, Belgium

Email:
stefaan.vaes@wis.kuleuven.be

DOI:
http://dx.doi.org/10.1090/S0002-9947-2012-05415-8

Received by editor(s):
June 15, 2010

Received by editor(s) in revised form:
July 6, 2010

Published electronically:
January 6, 2012

Additional Notes:
The first author was supported by ERC Starting Grant VNALG-200749.

The second author was partially supported by ERC Starting Grant VNALG-200749, Research Programme G.0231.07 of the Research Foundation, Flanders (FWO) and K. U. Leuven BOF research grant OT/08/032.

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.