scholarly journals Finite factor representations of Higman–Thompson groups

2014 ◽  
Vol 8 (2) ◽  
pp. 375-389 ◽  
Author(s):  
Artem Dudko ◽  
Konstantin Medynets
Keyword(s):  
Thompson Groups ◽  
Finite Factor

scholarly journals Local rigidity for actions of Kazhdan groups on noncommutative Lp-spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550064
Author(s):  
Bachir Bekka
Keyword(s):  
Von Neumann Algebra ◽  
Regular Representation ◽  
Von Neumann ◽  
Lp Spaces ◽  
Local Rigidity ◽  
Left Regular Representation ◽  
Left Regular ◽  
Property T ◽  
Finite Factor ◽  
Finite Index Subgroup

Let Γ be a discrete group and 𝒩 a finite factor, and assume that both have Kazhdan's Property (T). For p ∈ [1, +∞), p ≠ 2, let π : Γ →O(Lp(𝒩)) be a homomorphism to the group O(Lp(𝒩)) of linear bijective isometries of the Lp-space of 𝒩. There are two actions πl and πr of a finite index subgroup Γ+ of Γ by automorphisms of 𝒩 associated to π and given by πl(g)x = (π(g) 1)*π(g)(x) and πr(g)x = π(g)(x)(π(g) 1)* for g ∈ Γ+ and x ∈ 𝒩. Assume that πl and πr are ergodic. We prove that π is locally rigid, that is, the orbit of π under O(Lp(𝒩)) is open in Hom (Γ, O(Lp(𝒩))). As a corollary, we obtain that, if moreover Γ is an ICC group, then the embedding g ↦ Ad (λ(g)) is locally rigid in O(Lp(𝒩(Γ))), where 𝒩(Γ) is the von Neumann algebra generated by the left regular representation λ of Γ.

Divergence functions of Thompson groups

2018 ◽  
Vol 201 (1) ◽  
pp. 227-242
Author(s):  
Gili Golan ◽  
Mark Sapir
Keyword(s):  
Thompson Groups

scholarly journals Higher dimensional generalizations of the Thompson groups

2020 ◽  
Vol 369 ◽  
pp. 107191
Author(s):  
Mark V. Lawson ◽  
Alina Vdovina
Keyword(s):  
Thompson Groups ◽  
Higher Dimensional

scholarly journals On the Haagerup and Kazhdan properties of R. Thompson’s groups

2019 ◽  
Vol 22 (5) ◽  
pp. 795-807 ◽  
Author(s):  
Arnaud Brothier ◽  
Vaughan F. R. Jones
Keyword(s):  
Commutator Subgroup ◽  
Invariant Vector ◽  
Haagerup Property ◽  
Thompson Groups ◽  
Thompson's Groups ◽  
Intermediate Subgroup ◽  
Regular Representations ◽  
Left Regular ◽  
Invariant Vectors ◽  
Property T

Abstract A machinery developed by the second author produces a rich family of unitary representations of the Thompson groups F, T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V that has an almost invariant vector but no nonzero {[F,F]} -invariant vectors reproving and extending Reznikoff’s result that any intermediate subgroup between the commutator subgroup of F and V does not have Kazhdan’s property (T) (though Reznikoff proved it for subgroups of T). Second, we construct a one parameter family interpolating between the trivial and the left regular representations of V. We exhibit a net of coefficients for those representations which vanish at infinity on T and converge to 1 thus reproving that T has the Haagerup property after Farley who further proved that V has this property.

scholarly journals The homology of the Higman–Thompson groups

2019 ◽  
Vol 216 (2) ◽  
pp. 445-518 ◽  
Author(s):  
Markus Szymik ◽  
Nathalie Wahl
Keyword(s):  
Thompson Groups

scholarly journals On Jones’ subgroup of R. Thompson’s group T

2018 ◽  
Vol 28 (05) ◽  
pp. 877-903
Author(s):  
Jordan Nikkel ◽  
Yunxiang Ren
Keyword(s):  
Unitary Representation ◽  
Unitary Representations ◽  
Thompson Groups ◽  
Diagram Groups ◽  
Thompson’S Group ◽  
Planar Algebra ◽  
Thompson Group

Jones introduced unitary representations for the Thompson groups [Formula: see text] and [Formula: see text] from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups [Formula: see text] and [Formula: see text]. Golan and Sapir studied [Formula: see text] and identified it as a copy of the Thompson group [Formula: see text]. In this paper, we completely describe [Formula: see text] and show that [Formula: see text] coincides with its commensurator in [Formula: see text], implying that the corresponding unitary representation is irreducible. We also generalize the notion of the Stallings 2-core for diagram groups to [Formula: see text], showing that [Formula: see text] and [Formula: see text] are not isomorphic, but as annular diagram groups they have very similar presentations.

scholarly journals On continuity of the index of subfactors of a finite factor

1988 ◽  
Vol 76 (1) ◽  
pp. 56-66
Author(s):  
Bahman Mashhood ◽  
Keith F Taylor
Keyword(s):  
Finite Factor
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