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

作者：Houdayer Cyril^*; Popa Sorin; Vaes Stefaan

来源：Groups, Geometry, and Dynamics, 2013, 7(3): 577-590.

DOI：10.4171/GGD/198

• W*-superrigidity
• deformation/rigidity theory
• II1 factor
• ergodic equivalence relation
• amalgamated free product group

We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A (sic) Gamma covering certain cases where Gamma is an amalgamated free product over a non-amenable subgroup. In combination with Kida's work we deduce that if Sigma < SL(3, Z) denotes the subgroup of matrices g with g(31) = g(32) = 0, then any free ergodic probability measure preserving action of Gamma = SL(3, Z)(*Sigma)SL(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.

• 出版日期2013