Rigidity for von Neumann Algebras and Their Invariants

Vaes, Stefaan

doi:10.1142/9789814324359_0113

Cited by 72 publications

(75 citation statements)

References 82 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…actions of countable groups (cf. the surveys in [11,24,34]). In comparison, our understanding of group von Neumann algebras LG is much more limited.…”

Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

W*-superrigidity for group von Neumann algebras of left-right wreath products

Berbec

Vaes

2013

Proceedings of the London Mathematical Society

Self Cite

View full text Add to dashboard Cite

We prove that for many nonamenable groups Γ, including all hyperbolic groups and all nontrivial free products, the left–right wreath product group 𝒢 ≔ (ℤ/2ℤ)(Γ) ⋊ (Γ×Γ) is W*‐superrigid. This means that the group von Neumann algebra L 𝒢 entirely remembers 𝒢. More precisely, if L 𝒢 is isomorphic with L Λ for an arbitrary countable group Λ, then Λ must be isomorphic with 𝒢.

show abstract

“…actions of countable groups (cf. the surveys in [11,24,34]). In comparison, our understanding of group von Neumann algebras LG is much more limited.…”

Section: Introduction and Statements Of The Main Resultsmentioning

confidence: 99%

W*-superrigidity for group von Neumann algebras of left-right wreath products

Berbec

Vaes

2013

Proceedings of the London Mathematical Society

Self Cite

View full text Add to dashboard Cite

show abstract

“…actions and their equivalence relations is the use of S. Popa's deformation/rigidity theory [Po07] within the framework of von Neumann algebras. This has led to a remarkable progress in understanding the equivalence relations and von Neumann algebras arising from certain classes of actions, including Bernoulli actions, see the surveys [Va10,Io12a,Io17].…”

Section: Introductionmentioning

confidence: 99%

Cocycle and orbit equivalence superrigidity for coinduced actions

Drimbe¹

2017

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that Σ < Γ are countable groups such that gΣg −1 ∩ Σ is finite for any g ∈ Γ \ Σ. Then any measure preserving action Σ X0 gives rise to a solidly ergodic equivalence relation if and only if the equivalence relation of the associated coinduced action Γ X is solidly ergodic. We continue by obtaining orbit equivalence rigidity for such actions by showing that the orbit equivalence relation of a rigid measure preserving action Σ X0 is "remembered" by the orbit equivalence relation of Γ X. As a corollary, by using [Io06b] we obtain a concrete family of uncountable many non-orbit equivalent free ergodic measure preserving actions of Z ≀ Fn, with n ≥ 2.

show abstract

“…Since then, many other examples have been discovered through combined efforts spawning from several directions of research including measurable methods group theory, geometric group theory, Popa's deformation/rigidity theory, or C *algebraic techniques [2, 24, 33, 36, 50, 53, 55, 66, 75, 77, 79, 82]. For further references and other related topics in OE we encourage the reader to consult the following excellent surveys [25,26,76,84,88].…”

Section: Introductionmentioning

confidence: 99%

OEandW* superrigidity results for actions by surface braid groups

Chifan

2015

Proc. London Math. Soc.

View full text Add to dashboard Cite

A. We show that several important normal subgroups Γ of the mapping class group of a surface satisfy the following property: any free, ergodic, probability measure preserving action Γ X is stably OE-superrigid. These include the central quotients of most surface braid groups and most Torelli groups and Johnson kernels. In addition, we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice-embeddings.Using these results in combination with previous results from [CIK13] we deduce that any free, ergodic, probability measure preserving action of almost any surface braid group is stably W * -superrigid, i.e., it can be completely reconstructed from its von Neumann algebra.

show abstract

Rigidity for von Neumann Algebras and Their Invariants

Cited by 72 publications

References 82 publications

W*-superrigidity for group von Neumann algebras of left-right wreath products

W*-superrigidity for group von Neumann algebras of left-right wreath products

Cocycle and orbit equivalence superrigidity for coinduced actions

OEandW* superrigidity results for actions by surface braid groups

Contact Info

Product

Resources

About