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 covering certain cases where is an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if < SL(3,) denotes the subgroup of matrices g with g31 = g32 = 0, then any free ergodic probability measure preserving action of = SL(3,) * SL(3,) is stably W*-superrigid. In the second part we settle a technical issue about the unitary conjugacy of group measure space Cartan subalgebras.
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