A class of superrigid group von Neumann algebras

DOI10.4007/annals.2013.178.1.4zbMath1295.46041arXiv1007.1412OpenAlexW2105841391MaRDI QIDQ355137

Adrian Ioana, Sorin Popa, Stefaan Vaes

Publication date: 24 July 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1412

zbMATH Keywords

von Neumann algebragroup algebrawreath productII\(_1\) factorsuperrigidity

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Special aspects of infinite or finite groups (20F99)

Related Items (46)

A class of \(\mathrm{II}_1\) factors with exactly two group measure space decompositions ⋮ Orbit equivalence rigidity of irreducible actions of right-angled Artin groups ⋮ Amenability versus non amenability: an introduction to von Neumann algebras ⋮ A remark on \(\mathbb{T}\)-valued cohomology groups of algebraic group actions ⋮ \(W^*\)-rigidity for the von Neumann algebras of products of hyperbolic groups ⋮ Classification results for nonsingular Bernoulli crossed products ⋮ Isomorphisms of algebras of convolution operators ⋮ OEandW* superrigidity results for actions by surface braid groups ⋮ Some unique group-measure space decomposition results ⋮ \(\mathrm{W}^*\)-rigidity paradigms for embeddings of \(\mathrm{II}_1\) factors ⋮ Charmenability of higher rank arithmetic groups ⋮ Measure equivalence rigidity via s-malleable deformations ⋮ One-cohomology and the uniqueness of the group measure space decomposition of a II\(_{1}\) factor ⋮ Uniqueness of the group measure space decomposition for Popa's \({\mathcal{HT}}\) factors ⋮ Some applications of group-theoretic Rips constructions to the classification of von Neumann algebras ⋮ Noncommutative ergodic theory of higher rank lattices ⋮ \(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ On unitary groups of crossed product von Neumann algebras ⋮ Von Neumann equivalence and properly proximal 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 ⋮ On solid ergodicity for Gaussian actions ⋮ A class of II\(_{1}\) factors with many non conjugate Cartan subalgebras ⋮ Structure of \(\mathrm{II}_{1}\) factors arising from free Bogoljubov actions of arbitrary groups ⋮ \(C^*\)-simplicity of locally compact Powers groups ⋮ W∗-superrigidity for coinduced actions ⋮ Amalgamated free product rigidity for group von Neumann algebras ⋮ Product rigidity in von Neumann and \(C^*\)-algebras via \(S\)-malleable deformations ⋮ Some OE- and \(W^{\ast}\)-rigidity results for actions by wreath product groups ⋮ On projective representations for compact quantum groups ⋮ Prime \(\mathrm{II}_1\) factors arising from irreducible lattices in products of rank one simple Lie groups ⋮ Unique Cartan decomposition for \(\mathrm{II}_1\) factors arising from arbitrary actions of free groups ⋮ Cocycle and orbit equivalence superrigidity for coinduced actions ⋮ \({C}^{\ast}\)-superrigidity of 2-step nilpotent groups ⋮ Representing interpolated free group factors as group 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 ⋮ Free nilpotent groups are 𝐶*-superrigid ⋮ CARTAN SUBALGEBRAS IN DIMENSION DROP ALGEBRAS ⋮ W*-superrigidity for wreath products with groups having positive first ℓ²-Betti number ⋮ \(\mathrm{W}^\ast\)-superrigidity for arbitrary actions of central quotients of braid groups ⋮ \(W^\ast\) and \(C^\ast \)-superrigidity results for coinduced groups ⋮ New examples of \({W}^\ast\) and \({C}^\ast \)-superrigid groups

Cites Work

• Group measure space decomposition of \(\text{II}_{1}\) factors and \(\text W^{*}\)-superrigidity
• Orbit equivalence, coinduced actions and free products
• Stable orbit equivalence of Bernoulli shifts over free groups
• Some rigidity results for non-commutative Bernoulli shifts
• Amalgamated free products of weakly rigid factors and calculation of their symmetry groups
• Bass-Serre rigidity results in von Neumann algebras
• Ergodic subequivalence relations induced by a Bernoulli action
• On a class of II\(_1\) factors with at most one Cartan subalgebra
• A model for real-time failure prognosis based on hidden Markov model and belief rule base
• \(L^{2}\)-rigidity in von Neumann algebras
• Free products of hyperfinite von Neumann algebras and free dimension
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Interpolated free group factors
• The stable rank of some free product \(C^*\)-algebras
• Rigidity of commensurators and irreducible lattices
• Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one
• One-cohomology and the uniqueness of the group measure space decomposition of a II\(_{1}\) factor
• Cocycle and orbit equivalence superrigidity for malleable actions of \(w\)-rigid groups
• Rigidity results for wreath product \(\mathrm{II}_1\) factors
• Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups
• Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. I
• Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. II
• On a class of type \(\text{II}_1\) factors with Betti numbers invariants
• Uncountably many \(II_1\) factors
• On rings of operators
• The unitary structure in finite rings of operators
• On rings of operators. IV
• Cocycle and orbit superrigidity for lattices in SL(n,R) acting on homogeneous spaces
• On the superrigidity of malleable actions with spectral gap
• W*–superrigidity for Bernoulli actions of property (T) groups
• Property T for von Neumann Algebras
• Explicit computations of all finite index bimodules for a family of II$_1$ factors
• There is no separable universal 𝐼𝐼₁-factor
• W*-superrigidity for group von Neumann algebras of left-right wreath products
• Two finite, non‐hyperfinite, non‐isomorphic factors
• A Kurosh-type theorem for type II1 factors
• "Problems in the Theory of Rings" Revisited
• The Units of Group-Rings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A class of superrigid group von Neumann algebras