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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
Posted: January 6, 2012
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Abstract: We prove that for a fairly large family of HNN extensions $\Gamma$ , the group measure space II factor $\textup {L}^\infty (X) \rtimes \Gamma$ given by an arbitrary free ergodic probability measure preserving action of $\Gamma$ 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 $\textup {L}^\infty (X) \rtimes \Gamma$ entirely remembers the group action from which it was constructed.

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