The regular representation of Neretin groups is factorial

Basile Morando

REVIEW 1 major objections 4 minor 3 cited by

The regular representation of Neretin groups is factorial

T0 review · 1 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The left regular representation of every Neretin group is factorial, giving the first non-discrete simple group whose von Neumann algebra is a factor.

desk verdict This paper proves factoriality of the regular representation of Neretin groups—the first such example for a non-discrete simple group—with a new and mostly sound criterion, though a real gap in a secondary Hecke-algebra application needs fixing. read the letter →

arxiv 2506.24029 v1 pith:G6HA5QUJ submitted 2025-06-30 math.OA math.GR

Basile Morando This is my paper · ORCID

classification math.OAmath.GR MSC 46L1022D2522D1020E08

keywords NeretingroupsfactorialregularrepresentationvonNeumannalgebrastotallydisconnectedlocallycompacttreealmostautomorphismtypeIIinfinityfactorscrossedproductsFouriercoefficientsongroup

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proves that the left regular representation of every Neretin group $N_{d,k}$ is factorial: the von Neumann algebra it generates has trivial center. Precisely, for the open amenable subgroup $O_{d,k}$ of local isometries, the commutant intersection $L(O_{d,k})' \cap L(N_{d,k})$ is just the scalars. From this the author concludes that $L(O_{d,k})$ is the hyperfinite $\mathrm{II}_{\infty}$ factor and $L(N_{d,k})$ is a type $\mathrm{II}_{\infty}$ factor. Since Neretin groups are abstractly simple, this provides the first example of a non-discrete simple group with factorial regular representation. The proof is built on a new, elementary factoriality criterion for totally disconnected locally compact groups, expressed through conjugation-orbit sizes of compact open subgroups.

What carries the argument

The argument is carried by Fourier coefficients on totally disconnected group von Neumann algebras: for $x \in L(G)$, the numbers $\hat{x}(gK) = \langle x\xi_K, \xi_{gK}\rangle$, where $K$ is a compact open subgroup and $\xi_A$ is the normalized indicator of a coset. These coefficients determine $x$ completely, and for $z \in L(H)' \cap L(G)$ they satisfy the key inequality $\|z\|_\infty^2 \geq c_H(gK)|\hat{z}(gK)|^2$, where $c_H(gK)$ is the cardinality of the orbit of $gK$ under conjugation by the normalizer $N_H(K)$. If $H$ lies in the modular kernel and the orbit sizes grow fast enough relative to Haar measure, this inequality forces every Fourier coefficient of $z$ away from the identity to vanish, so $z$ is scalar. For Neretin groups the verification uses two tree-boundary facts: any nontrivial local similarity can be isotoped so that $g(B_w) \cap B_w = \varnothing$ for some boundary ball $B_w$, and the rigid stabilizer of that ball in $O_{d,k}$ is large enough, giving the estimate $c_{O_{d,k}}(gK^{(n)}) \mu(K^{(n)})^2 \geq [(d^{n-n_0}/e)^{d^{n-n_0}}/(d!)^{d^{n-n_0}}] / [k!(d!)^{2kd^n}] \to \infty$.

What would settle it

The claim is settled by calculating, for a nontrivial local similarity $g$ and the standard compact open subgroups $K^{(n)}$, whether $c_{O_{d,k}}(gK^{(n)}) \mu(K^{(n)})^2$ really is unbounded; a single nontrivial $g$ for which this quantity stays bounded, or a pair $(d,k)$ for which the rigid-stabilizer index estimates fail, would break property $(\star_{O_{d,k}})$ and with it the proof of Theorem A.

Watch

Extended reading notes

Core claim

The central discovery is that the inclusion of $L(O_{d,k})$ in $L(N_{d,k})$ is irreducible in a strong sense: every operator in $L(N_{d,k})$ commuting with all of $L(O_{d,k})$ is a scalar, so $L(O_{d,k})' \cap L(N_{d,k}) = \mathbb{C}$. Consequently $L(N_{d,k})$ is a factor, and since both groups are unimodular the factor is of type $\mathrm{II}_{\infty}$; because $O_{d,k}$ is amenable, $L(O_{d,k})$ is the hyperfinite $\mathrm{II}_{\infty}$ factor. The general engine is a criterion applying to any totally disconnected locally compact group $G$ with a closed subgroup $H \leq \ker \Delta_G$: if there is a basis $(K_n)$ of compact open subgroups for which every nontrivial $g$ satisfies $\limsup_n c_H(gK_n) \mu_G(K_n)^2 = \infty$, then $L(H)' \cap L(G) = \mathbb{C}$. The author verifies this condition for the Neretin group with $H = O_{d,k}$ through explicit growth estimates comparing rigid stabilizers of boundary balls with the indices of the compact open subgroups.

Load-bearing premise

The proof stands or falls on the growth estimate $c_{O_{d,k}}(gK^{(n)}) \mu(K^{(n)})^2 \to \infty$ for every nontrivial $g$; this requires both that every nontrivial local similarity can be isotoped so that $g(B_w) \cap B_w = \varnothing$ for some boundary ball $B_w$, and that the rigid stabilizer of a boundary ball grows at the asserted factorial rate, so if either geometric fact fails for even one nontrivial element the lim sup condition in $(\star_H)$ fails and the criterion no longer applies.

Editorial extensions

If this is right

The group von Neumann algebra $L(N_{d,k})$ is a type $\mathrm{II}_{\infty}$ factor, and $L(O_{d,k})$ is the hyperfinite $\mathrm{II}_{\infty}$ factor, giving a new proof that both groups are not of type I.
The factoriality criterion applies to any closed subgroup of $N_{d,k}$ containing $O_{d,k}$, and to natural generalizations such as almost automorphism groups of regular branch groups, coloured Neretin groups, and piecewise full groups of profinite branch group actions.
For the visual boundary action, the crossed product $L^\infty(\partial T_{d,k}, \nu) \rtimes N_{d,k}$ is shown to be a type $\mathrm{III}_{1/d}$ factor.
The same orbit-counting methods yield factoriality for certain HNN extensions, including profinite completions of Baumslag–Solitar groups, and identify some Hecke von Neumann algebras of Burger–Mozes groups as interpolated free group factors.
Since $N_{d,k}$ and $O_{d,k}$ are not type I and are non-discrete, the factors $L(N_{d,k})$ and $L(O_{d,k})$ cannot be of type I, so their type is determined as $\mathrm{II}_{\infty}$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper leaves open whether $L(N_{d,k})$ is amenable; if a later argument established non-amenability, the result would give a simple totally disconnected group whose group factor is non-amenable, which would contrast with the amenable hyperfinite factor associated to $O_{d,k}$.
The criterion suggests a general route to factoriality for non-discrete groups: instead of approximating by discrete C*-simple groups, one can check orbit-growth estimates directly, making the method a candidate for other piecewise groups acting on Cantor sets.
Factoriality of the regular representation is strictly weaker than C*-simplicity, so the theorem should be read as evidence for, but not a proof of, C*-simplicity of Neretin groups, which remains open.
A testable extension would be to apply the same orbit-counting estimate to topological full groups of minimal Cantor actions, where the rigid stabilizer growth may be computable and could yield new factorial examples.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

The headline: this paper proves that Neretin groups have factorial left regular representation, the first example for a non-discrete simple group, and it does so with a genuinely new and elementary criterion. The main theorem and its supporting estimates are sound as far as I can tell. There is one real flaw, but it sits in a secondary application and does not touch the central result.

What is new: Theorem B is a Fourier-coefficient criterion for factoriality of L(G) for tdlc groups, based on conjugation-orbit growth c_H(gK_n) μ(K_n)^2. The proof via averaging projections and the inequality in Lemma 1.7 is clean. The Neretin application is not a formality: it requires the explicit lower bound c_{O_{d,k}}(g K^{(n)}) μ(K^{(n)})^2 ≥ [(d^m/e)^{d^m}/(d!)^{d^m}] / [k!(d!)^{2kd^n}] → ∞. That estimate uses the rigid stabilizer index and the standard fact that a nontrivial local similarity can be pushed off a ball. I checked the index bookkeeping and the modular factor in Lemma 1.7; it is consistent. Corollary C's type argument is a nice byproduct, and Theorem D's crossed-product version is a natural extension. The paper is also honest about what it does not claim: Section 1.5 says the HNN consequences are essentially reformulations of Raum and Suzuki.

The soft spot is Proposition 1.13. The proof asserts that if N = N_A(K)_0 has quotient N/K of order ≤ 2, then N is a compact open normal subgroup of N_A(K), hence N_A(K) = N. That implication is false: a compact open normal subgroup can have infinite quotient, and the modular character can be infinite cyclic. The Hecke-algebra applications to amalgamated free products and Burger–Mozes groups rest on this proposition, so those corollaries are not justified as written. This looks repairable—one would need a different argument or an additional hypothesis—but it is a genuine gap, not a typo. It does not enter the proofs of Theorems A, B, or D.

Who should read it: anyone working on type I/II questions for tdlc groups, or on Neretin groups and simple locally compact groups. The main theorem will be cited. I would send it to a serious referee: the central claim is important and the proof is detailed enough to verify. I would ask the referee to focus on fixing or isolating the Proposition 1.13 issue before publication.

Recommended action: referee, with revision expected.

Referee Report

1 major / 4 minor

Summary. The paper introduces a factoriality criterion for the left regular representation of totally disconnected locally compact groups. Theorem B (Theorem 1.9) states that if a closed subgroup H of G lies in ker Δ_G and there is a compact-open neighborhood basis (K_n) such that limsup_n c_H(gK_n) μ_G(K_n)^2 = ∞ for every nontrivial g, then L(H)'∩L(G)=C. The main application is to Neretin groups N_{d,k}: with H=O_{d,k} and K_n=K_{d,k}^{(n)}, explicit rigid-stabilizer estimates are used to verify the criterion, yielding L(O_{d,k})'∩L(N_{d,k})=C. Theorem A (Theorem 1.19) then identifies L(N_{d,k}) and L(O_{d,k}) as type II_∞ factors, giving the first example of a non-discrete simple group whose regular representation is factorial. The paper also derives type consequences, applies the criterion to Hecke von Neumann algebras of amalgamated free products, to HNN extensions of locally compact groups, and proves a crossed-product analogue (Theorem D) with an application to the action of N_{d,k} on the visual boundary.

Significance. The main result is substantial and original. It settles the factoriality question for Neretin groups, identifies the type of the resulting factors, and provides the first known example of a non-discrete simple group with factorial group von Neumann algebra. The proof is elementary and self-contained, with explicit lower bounds and no fitted parameters or circularity; it relies only on standard external results. The general criterion Theorem B is likely to be useful beyond Neretin groups, and the crossed-product theorem gives new factorial type III examples. The secondary applications, especially the Hecke-algebra results for Burger-Mozes groups, are interesting but contain a proof gap discussed below.

major comments (1)

[§1.4, Proposition 1.13] The proof of Proposition 1.13 contains an unjustified step. Let N_A(K)_0 denote the kernel of the modular function restricted to N_A(K). The proof asserts that if |N_A(K)_0/K|≤2, then N_A(K)_0 is a compact open normal subgroup of N_A(K), "therefore" N_A(K)=N_A(K)_0. This implication is false: a compact open normal subgroup need not be the whole group. For a concrete example, take K=Z_p and A=K⋊Z with the Z-action by multiplication by p; then K is compact open in A, N_A(K)=A, N_A(K)_0=K, and |N_A(K)/K|=∞ while |N_A(K)_0/K|=1. The hypotheses of the proposition can be met in this situation by taking B=K×C_2, so |N_B(K)/K|=2. The subsequent construction of elements a_1,a_2∈N_A(K)_0\K then fails in general. Since Proposition 1.8 requires the relevant subgroup to be contained in ker Δ_G, the reduction to the unimodular part is not justified without an additional hypothesis (for example, unimodularity of A and B, which does hold in the intended Burger-Mozes application where the vertex groups are compact). As stated, the proof of Proposition 1.13 does not establish the factoriality of p_K L(G)p_K, and Corollary 1.14 and Example 1.15 inherit this gap.

minor comments (4)

[§1.1] Page 6 contains a duplicated phrase: "endowed with endowed its Plancherel weight" should be "endowed with its Plancherel weight".
[§1.4, Proposition 1.13] The notation "N_A(K)_0 = N_A∩ker Δ_G(K)" is ill-formed; the modular function is on G, so the intended meaning is presumably the kernel of Δ_G restricted to N_A(K), or equivalently the unimodular part of N_A(K). The definition should be stated unambiguously.
[§2.2, Proposition 2.4] In the proof of the second part of Proposition 2.4, the expression "[x−a(gK)=0" is garbled; it should read "\widehat{x-a}(gK)=0".
[§1.6, Theorem 1.19] The geometric assertion that, for every nontrivial local similarity g, one can find a ball B_w with g(B_w)∩B_w=∅ is stated without proof; a one-sentence justification would improve readability, although the claim is standard and correct.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the factoriality of the Neretin regular representation follows from an explicit growth estimate, not from its conclusion.

full rationale

The central claim, Theorem A (Theorem 1.19), is derived from a general criterion, Theorem B (Theorem 1.9), and the paper then verifies the hypothesis (star_H) for H = O_{d,k} by an explicit combinatorial lower bound. The verification is self-contained: for nontrivial g it exhibits a ball B_w with g(B_w) disjoint from B_w, defines H(w,n) and L_w, and computes the index [H(w,n):L_w] = [O_{d,d}^{(n-n0)} : K_{d,d}] together with bounds on [K_{d,d}:K_{d,d}^{(n-n0)}] and [K_{d,k}:K_{d,k}^{(n)}]. The resulting estimate c_{O_{d,k}}(gK^{(n)}) mu(K^{(n)})^2 grows at least like (d^{n-n0}/e)^{d^{n-n0}}/(d!)^{d^{n-n0}} times a negative power of k!(d!)^{2kd^n}, which tends to infinity. This is a direct proof of the criterion's hypothesis; no fitted parameter is renamed as a prediction, and the conclusion L(O_{d,k})' cap L(N_{d,k}) = C is not assumed anywhere. External citations are used only for standard facts (Takesaki, Connes, Haagerup) and for background on Neretin groups; none of these citations is by the present author or carries the load of the main argument. The paper even notes its independent proof of known non-type-I results for N_{d,k} and O_{d,k}, so those citations are corroborative rather than load-bearing. The secondary issue noted by the reader concerning Proposition 1.13 affects only the Hecke-algebra application in Section 1.4 and does not enter the proofs of Theorem B, Theorem A, or Corollary C. No self-referential or circular pattern is present in the derivation chain.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central proof rests on standard operator algebra theorems and on geometric facts specific to the action of Neretin groups on the tree boundary. No free parameters are fitted; the only quantitative inputs are explicit indices and growth rates. The assumptions listed are the main external foundations; the structural tree facts are proved in the text.

assumptions (6)

standard math Takesaki's theorem that L(G)=rho_G(G)' for locally compact G
Used to commute elements of L(H)' with right translations in Lemma 1.7; cited to [Tak03, Proposition VII.3.1].
standard math Bicommutant theorem and identification of L(H) with a subalgebra of L(G)
Used throughout to treat L(H) as a von Neumann subalgebra of L(G); cited to [Miy25, Proposition 2.1].
standard math Compact open subgroups form a neighborhood basis in tdlc groups (van Dantzig)
Basis for the net (p_K) and for property (⋆_H); standard.
standard math Amenability of O_{d,k} and Connes-Haagerup classification of amenable factors
To conclude L(O_{d,k}) is the hyperfinite II_infinity factor; O_{d,k} is a countable union of compact open subgroups, hence amenable.
domain assumption Uniqueness and local compactness of the Neretin group topology with K_{d,k} compact open
Imported from [LB17, Lemme 4.3]; must hold for the measure normalization and the basis (K^{(n)}) to make sense.
domain assumption Structural facts about O^{(n)}, K^{(n)}, and rigid stabilizers in the tree boundary
Used in the growth estimate in the proof of Theorem 1.19; asserted without a separate proof, but follows from the tree geometry.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The regular representation of Neretin groups is factorial." pith.science (2026). https://pith.science/paper/G6HA5QUJ

@misc{pith2026250624029,
  author       = {Pith},
  title        = {Pith review of: The regular representation of Neretin groups is factorial},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G6HA5QUJ}},
  note         = {Machine review of arXiv:2506.24029}
}

read the original abstract

We show that the left regular representation of Neretin groups is factorial, providing the first example of a non-discrete simple group with this property. This is based on a new criterion of factoriality for totally disconnected groups. For groups G satisfying the criterion, we determine the type of the factor L(G) and derive factoriality results for crossed products associated to G-actions on von Neumann algebras.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On ergodicity of linear actions on $\mathbb{R}^n$ and factoriality of group von Neumann algebras
math.OA 2025-10 conditional novelty 7.0 of 10

For split actions of countable groups on abelian Lie-type groups, faithful dually ergodic or doubly ergodic linear part plus infinite orbits or finite stabilizers on the discrete part makes L(N⋊Γ) a factor; and a coun...
Non-strong ergodicity of canonical actions of the Thompson groups
math.DS 2025-10 conditional novelty 6.0 of 10

Canonical actions of Thompson's group V and topological full groups of amenable ample groupoids on the Cantor set are not strongly ergodic, so their crossed products are non-full factors (type III_{1/d} for Higman–Thompson).
Projective representations of almost unimodular groups
math.OA 2025-09 conditional novelty 6.0 of 10

Formal degree and Atiyah-Schmid dimension formulas hold for square integrable projective representations of second countable almost unimodular groups with a 2-cocycle twist.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · cited by 3 Pith papers

[1]

On the type of the von Neumann algebra of an open subgroup of the Neretin group

[Ari22] Ryoya Arimoto. “On the type of the von Neumann algebra of an open subgroup of the Neretin group”. In:Proc. Amer. Math. Soc. Ser. B9 (2022), pp. 311–316. [Ari25] Ryoya Arimoto. “Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries”. In:J. Funct. Anal.288.3 (2025), Paper No. 110732,

work page 2022
[6]

Hecke C∗-algebras and amenability

Springer-Verlag, Berlin, 2003, pp. xxii+518. [Tza03] Kroum Tzanev. “Hecke C∗-algebras and amenability”. In: J. Operator Theory 50.1 (2003), pp. 169–178. [Vae25] Stefaan Vaes. Factoriality of twisted locally compact group von Neumann algebras

work page 2003
[11]

The regular representation of restricted direct product groups

NewMathematicalMonographs.CambridgeUniversityPress,Cambridge,2008,pp.xiv+472. [Bla77] Bruce E. Blackadar. “The regular representation of restricted direct product groups”. In: J. Functional Analysis25.3 (1977), pp. 267–274. [BM00] MarcBurgerandShaharMozes.“Groupsactingontrees:fromlocaltoglobalstructure”. In: Inst. Hautes Études Sci. Publ. Math.92 (2000), ...

work page 1977
[12]

Factoriality of twisted locally compact group von Neumann algebras

arXiv: 2412.15733 [math.OA]. [Zhe19] Tianyi Zheng. Neretin groups admit no non-trivial invariant random subgroups

work page Pith review arXiv
[16]

Simple groups without lattices

[Bad12] Uri Bader, Pierre-Emmanuel Caprace, Tsachik Gelander, and Shahar Mozes. “Simple groups without lattices”. In:Bull. Lond. Math. Soc.44.1 (2012), pp. 55–67. [BB24] Ingrid Beltiţă and Daniel Beltiţă. “On the regular representation of solvable Lie groups with open coadjoint quasi-orbits”. In:Anal. Math. Phys.14.4 (2024), Paper No. 81,

work page 2012
[25]

Piecewise strongly proximal actions, free boundaries and the Neretin groups

EMS Tracts in Mathematics. Winner of the 2016 EMS Monograph Award. European Mathematical Society (EMS), Zürich, 2016, pp. viii+235. [CLM22] Pierre-Emmanuel Caprace, Adrien Le Boudec, and Nicolás Matte Bon. “Piecewise strongly proximal actions, free boundaries and the Neretin groups”. In:Bull. Soc. Math. France150.4 (2022), pp. 773–795. [Con73] Alain Conne...

work page 2022
[89]

Springer-Verlag, Berlin-New York, 1977, pp

Ergeb- nisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]. Springer-Verlag, Berlin-New York, 1977, pp. xiv+339. [Miy25] Yuki Miyamoto. Analysis of the Plancherel weight and factoriality of the group von Neumann algebras of non-unimodular totally disconnected groups

work page 1977
[161]

Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index

[Răd94] Florin Rădulescu. “Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index”. In:Invent. Math. 115.2 (1994), pp. 347–389. [Rau19] Sven Raum. “ C∗-simplicity of locally compact Powers groups”. In:J. Reine Angew. Math. 748 (2019), pp. 173–205. [Rau21] Sven Raum. In: Journal für die rei...

work page 1994

Show all 13 references

[250]

American Mathematical Society, Providence, RI, 2020, pp

Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2020, pp. xi+474. [BHV08] Bachir Bekka, Pierre de la Harpe, and Alain Valette.Kazhdan’s property (T). Vol

2020
[447]

Murray–von Neumann di- mension for strictly semifinite weights

London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 2018, pp. 131–144. [GLN25] Aldo Garcia Guinto, Matthew Lorentz, and Brent Nelson. “Murray–von Neumann di- mension for strictly semifinite weights”. In:J. Funct. Anal.289.5 (2025), Paper No. 110938,

2025
[2019]

arXiv: 1905.07605 [math.GR]. 22

1905 arXiv
[2025]

The standard form of von Neumann algebras

arXiv:2501.00908 [math.GR]. [Haa75] Uffe Haagerup. “The standard form of von Neumann algebras”. In:Math. Scand.37.2 (1975), pp. 271–283. [HR19] Cyril Houdayer and Sven Raum. “Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras”. ...

1975 arXiv
[2505]

C∗-simplicityofrelativeprofinitecompletionsofgeneralizedBaumslag- Solitar groups

21253 [math.OA]. [Muk24] MihoMukohara.“ C∗-simplicityofrelativeprofinitecompletionsofgeneralizedBaumslag- Solitar groups”. In:Publ. Res. Inst. Math. Sci.60.2 (2024), pp. 351–372. [MV36] F. J. Murray and J. Von Neumann. “On rings of operators”. In:Ann. of Math. (2)37.1 (1936), ...

2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

On the type of the von Neumann algebra of an open subgroup of the Neretin group

[Ari22] Ryoya Arimoto. “On the type of the von Neumann algebra of an open subgroup of the Neretin group”. In:Proc. Amer. Math. Soc. Ser. B9 (2022), pp. 311–316. [Ari25] Ryoya Arimoto. “Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries”. In:J. Funct. Anal.288.3 (2025), Paper No. 110732,

work page 2022

[2] [6]

Hecke C∗-algebras and amenability

Springer-Verlag, Berlin, 2003, pp. xxii+518. [Tza03] Kroum Tzanev. “Hecke C∗-algebras and amenability”. In: J. Operator Theory 50.1 (2003), pp. 169–178. [Vae25] Stefaan Vaes. Factoriality of twisted locally compact group von Neumann algebras

work page 2003

[3] [11]

The regular representation of restricted direct product groups

NewMathematicalMonographs.CambridgeUniversityPress,Cambridge,2008,pp.xiv+472. [Bla77] Bruce E. Blackadar. “The regular representation of restricted direct product groups”. In: J. Functional Analysis25.3 (1977), pp. 267–274. [BM00] MarcBurgerandShaharMozes.“Groupsactingontrees:fromlocaltoglobalstructure”. In: Inst. Hautes Études Sci. Publ. Math.92 (2000), ...

work page 1977

[4] [12]

Factoriality of twisted locally compact group von Neumann algebras

arXiv: 2412.15733 [math.OA]. [Zhe19] Tianyi Zheng. Neretin groups admit no non-trivial invariant random subgroups

work page Pith review arXiv

[5] [16]

Simple groups without lattices

[Bad12] Uri Bader, Pierre-Emmanuel Caprace, Tsachik Gelander, and Shahar Mozes. “Simple groups without lattices”. In:Bull. Lond. Math. Soc.44.1 (2012), pp. 55–67. [BB24] Ingrid Beltiţă and Daniel Beltiţă. “On the regular representation of solvable Lie groups with open coadjoint quasi-orbits”. In:Anal. Math. Phys.14.4 (2024), Paper No. 81,

work page 2012

[6] [25]

Piecewise strongly proximal actions, free boundaries and the Neretin groups

EMS Tracts in Mathematics. Winner of the 2016 EMS Monograph Award. European Mathematical Society (EMS), Zürich, 2016, pp. viii+235. [CLM22] Pierre-Emmanuel Caprace, Adrien Le Boudec, and Nicolás Matte Bon. “Piecewise strongly proximal actions, free boundaries and the Neretin groups”. In:Bull. Soc. Math. France150.4 (2022), pp. 773–795. [Con73] Alain Conne...

work page 2022

[7] [89]

Springer-Verlag, Berlin-New York, 1977, pp

Ergeb- nisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]. Springer-Verlag, Berlin-New York, 1977, pp. xiv+339. [Miy25] Yuki Miyamoto. Analysis of the Plancherel weight and factoriality of the group von Neumann algebras of non-unimodular totally disconnected groups

work page 1977

[8] [161]

Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index

[Răd94] Florin Rădulescu. “Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index”. In:Invent. Math. 115.2 (1994), pp. 347–389. [Rau19] Sven Raum. “ C∗-simplicity of locally compact Powers groups”. In:J. Reine Angew. Math. 748 (2019), pp. 173–205. [Rau21] Sven Raum. In: Journal für die rei...

work page 1994