HNN extensions and unique group measure space decomposition of II_1 factors

Details HNN extensions and unique group measure space decomposition of II_1 factors HNN extensions and unique group measure space decomposition of II_1 factors

2010-05-27

arxiv.org/abs/1005.5002v2

Transactions of the American Mathematical Society 364 (2012), 2601-2617

Mathematics

Operator Algebras

Remarks added, final version, to appear in Trans. Amer. Math. Soc

Scientific paper

We prove that for a fairly large family of HNN extensions \Gamma, the group measure space II_1 factor 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. We deduce from this new examples of W^*-superrigid group actions, i.e. where the II_1 factor L^\infty(X) \rtimes \Gamma entirely remembers the group action that it was constructed from.

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