On L1-approximation of groups

Benjamin Bachner; Alon Dogon; Alexander Lubotzky

doi:10.1016/j.jalgebra.2026.04.041

On L¹-approximation of groups

Benjamin Bachner
, Alon Dogon^*
, Alexander Lubotzky

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

A longstanding open problem in the intersection of group theory and operator algebras is whether all groups are MF, that is, approximated by asymptotic representations with respect to the operator norm. More generally, in his ICM address from 2018, Thom asked whether there exist groups that are not approximated with respect to the Schatten p-norm for 1≤p≤∞. The cases of 1<p<∞ were addressed in previous works of De Chiffre et al. and Lubotzky-Oppenheim. Here we settle the case p=1.

Original language	English
Pages (from-to)	235-243
Number of pages	9
Journal	Journal of Algebra
Volume	702
DOIs	https://doi.org/10.1016/j.jalgebra.2026.04.041
State	Published - 15 Sep 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2026 Elsevier Inc.

Keywords

Hyperlinear groups
MF groups
Property (T)
Sofic groups
p-Schatten norm

Access to Document

10.1016/j.jalgebra.2026.04.041

Cite this

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