Geodesic
A class of groups for which every action is W$^*$-superrigid
Cyril Houdayer1 ; Sorin Popa2 ; Stefaan Vaes3
1École Normale Supérieure de Lyon, France
2University of California Los Angeles, United States
3Katholieke Universiteit Leuven, Belgium
Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 577-590

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DOI

We prove the uniqueness of the group measure space Cartan subalgebra in crossed products A⋊Γ covering certain cases where Γ is 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 g31​=g32​=0, then any free ergodic probability measure preserving action of Γ=SL(3,Z)∗Σ​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.
DOI : 10.4171/ggd/198
Classification : 46-XX, 20-XX, 37-XX
Mots-clés : W*-superrigidity, deformation/rigidity theory, II1​ factor, ergodic equivalence relation, amalgamated free product group

Cyril Houdayer  1   ; Sorin Popa  2   ; Stefaan Vaes  3

1 École Normale Supérieure de Lyon, France
2 University of California Los Angeles, United States
3 Katholieke Universiteit Leuven, Belgium 
Cyril Houdayer; Sorin Popa; Stefaan Vaes. A class of groups for which every action is W$^*$-superrigid. Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 577-590. doi: 10.4171/ggd/198
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     title = {A class of groups for which every action is {W}$^*$-superrigid},
     journal = {Groups, geometry, and dynamics},
     pages = {577--590},
     year = {2013},
     volume = {7},
     number = {3},
     doi = {10.4171/ggd/198},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/198/}
}
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