A class of groups for which every action is W*-superrigid

Abstract

We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A \rtimes Γcovering certain cases where Γis an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if Σ< SL(3,\Z) denotes the subgroup of matrices g with g_31 = g_32 = 0, then any free ergodic probability measure preserving action of Γ= SL(3,\Z) *_ΣSL(3,\Z) is stably W*-superrigid. In the second part we settle a technical issue about the unitary conjugacy of group measure space Cartan subalgebras.

v3: Minor changes; final version; to appear in Groups, Geometry, and Dynamics v2: We changed the title to make it more informative

References in corpus (1)

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

Cited by in corpus (3)

• One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor
• W*-superrigidity of mixing Gaussian actions of rigid groups
• Uniqueness of group-measure space Cartan subalgebras