The Dixmier problem, lamplighters and Burnside groups

Monod, Nicolas; Ozawa, Narutaka

doi:10.1016/j.jfa.2009.06.029

Cited by 29 publications

(32 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Combining Theorems 1 and 2 with the main result of ref. 36, we conclude that the wreath product Z ≀ H is a torsion-free nonunitarisable group without free subgroups. We can replace it by a finitely generated subgroup upon choosing a nonamenable, finitely generated subgroup of H. This construction provides some new examples to Dixmier's problem, unsolved since 1950 (37)(38)(39).…”

mentioning

confidence: 66%

Groups of piecewise projective homeomorphisms

Monod

2013

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 66%

Groups of piecewise projective homeomorphisms

Monod

2013

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, in view of Theorem 1.1, Dixmier's problem is equivalent to the conjunction of Question 8.7 with the following. There is however a form of overlap between these two questions, as can be shown using the main result of [24], as follows.…”

Section: B Burnside Groupsmentioning

confidence: 99%

Asymptotics of Cheeger constants and unitarisability of groups

Герасимова

Gruber

Monod³

et al. 2020

Journal of Functional Analysis

Self Cite

View full text Add to dashboard Cite

Given a group Γ, we establish a connection between the unitarisability of its uniformly bounded representations and the asymptotic behaviour of the isoperimetric constants of Cayley graphs of Γ for increasingly large generating sets.The connection hinges on an analytic invariant Lit(Γ) ∈ [0, ∞] which we call the Littlewood exponent. Finiteness, amenability, unitarisability and the existence of free subgroups are related respectively to the thresholds 0, 1, 2 and ∞ for Lit(Γ). Using graphical small cancellation theory, we prove that there exist groups Γ for which 1 < Lit(Γ) < ∞. Further applications, examples and problems are discussed. Contents

show abstract

“…The Dixmier problem asks whether the converse holds true (see, for instance, [14]). In [13], Monod The restricted second nilpotent wreath product…”

Section: Introductionmentioning

confidence: 99%

Permanence properties of the second nilpotent product of groups

Sasyk¹

2019

Bull. Belg. Math. Soc. Simon Stevin

View full text Add to dashboard Cite

We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a semi-direct product akin to the restricted wreath product but constructed from the second nilpotent product. We then show that if two discrete groups have the Haagerup property, the restricted second nilpotent wreath product of them also has the Haagerup property. We finally show that if a discrete group is abelian, then the restricted second nilpotent wreath product constructed from it is unitarizable if and only if the acting group is amenable.

show abstract

The Dixmier problem, lamplighters and Burnside groups

Cited by 29 publications

References 9 publications

Groups of piecewise projective homeomorphisms

Groups of piecewise projective homeomorphisms

Asymptotics of Cheeger constants and unitarisability of groups

Permanence properties of the second nilpotent product of groups

Contact Info

Product

Resources

About