A class of groups for which every action is W\(^\ast\)-superrigid

DOI10.4171/GGD/198zbMath1314.46072arXiv1010.5077MaRDI QIDQ374099

Stefaan Vaes, Cyril Houdayer, Sorin Popa

Publication date: 28 October 2013

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.5077

zbMATH Keywords

II\(_1\) factoramalgamated free product groupdeformation/rigidity theoryergodic equivalence relationW\(^\ast\)-superrigidity

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Classification of factors (46L36)

Related Items (23)

Unitary conjugacy for type III subfactors and \(W^\ast\)-superrigidity ⋮ Tensor product decompositions of \(\mathrm{II}_1\) factors arising from extensions of amalgamated free product groups ⋮ Ergodic group theory ⋮ OEandW* superrigidity results for actions by surface braid groups ⋮ Explicit examples of equivalence relations and II₁ factors with prescribed fundamental group and outer automorphism group ⋮ Uniqueness of the group measure space decomposition for Popa's \({\mathcal{HT}}\) factors ⋮ Invariant subalgebras of von Neumann algebras arising from negatively curved groups ⋮ Compact actions and uniqueness of the group measure space decomposition of II\(_{1}\) factors ⋮ Orbit equivalence rigidity for product actions ⋮ Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces ⋮ \(W^\ast\)-superrigidity of mixing Gaussian actions of rigid groups ⋮ On the structural theory of \(\mathrm{II}_1\) factors of negatively curved groups. II: Actions by product groups ⋮ A class of II\(_{1}\) factors with many non conjugate Cartan subalgebras ⋮ Normalizers inside amalgamated free product von Neumann algebras ⋮ HNN extensions and unique group measure space decomposition of II$_{1}$ factors ⋮ W∗-superrigidity for coinduced actions ⋮ Amalgamated free product rigidity for group von Neumann algebras ⋮ Cocycle and orbit equivalence superrigidity for coinduced actions ⋮ Unbounded derivations, free dilations, and indecomposability results for II$_1$ factors ⋮ Prime \(\text{II}_1\) factors arising from actions of product groups ⋮ Some rigidity results for \(II_1\) factors arising from wreath products of property (T) groups ⋮ \(\mathrm{W}^\ast\)-superrigidity for arbitrary actions of central quotients of braid groups ⋮ New examples of \({W}^\ast\) and \({C}^\ast \)-superrigid groups

Cites Work

• Rigidity of amalgamated free products in measure equivalence
• Property T for von Neumann Algebras
• HNN extensions and unique group measure space decomposition of II$_{1}$ factors
• Groups with the Haagerup property. Gromov's a-T-menability

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