HNN extensions and unique group measure space decomposition of II_1 factors

Abstract

We prove that for a fairly large family of HNN extensions Γ, the group measure space II_1 factor L^\infty(X) \rtimes Γgiven by an arbitrary free ergodic probability measure preserving action of Γ, 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 Γentirely remembers the group action that it was constructed from.

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

References in corpus (1)

• Examples of group actions which are virtually W*-superrigid

Cited by in corpus (3)

• One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor
• A class of groups for which every action is W*-superrigid
• A class of II_1 factors with many non conjugate Cartan subalgebras