[Le théorème du facteur non commutatif pour des réseaux dans des groupes produits]
We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible lattices in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary.
Nous montrons un théorème du facteur de Bader-Shalom non commutatif pour les réseaux avec des projections denses dans les groupes produits. Comme application de ce résultat et de nos travaux précédents, nous obtenons un théorème du facteur de Margulis non commutatif pour tous les réseaux irréductibles dans les groupes algébriques semi-simples de rang supérieur. En particulier, nous donnons une description complète de toutes les sous-algèbres de von Neumann intermédiaires situées entre l’algèbre de von Neumann de groupe et l’algèbre de von Neumann d’espace de mesure de groupe associée à l’action sur le bord de Furstenberg-Poisson.
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Keywords: Factor theorem, Furstenberg-Poisson boundaries, group measure space von Neumann algebras, higher rank lattices in semisimple algebraic groups
Mots-clés : Théorème du facteur, bords de Furstenberg-Poisson, algèbres de von Neumann d’espace de mesure de groupe, groupes algébriques semi-simples de rang supérieur
Boutonnet, Rémi 1 ; Houdayer, Cyril 2
CC-BY 4.0
@article{JEP_2023__10__513_0,
author = {Boutonnet, R\'emi and Houdayer, Cyril},
title = {The noncommutative factor theorem for lattices in product groups},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {513--524},
year = {2023},
publisher = {Ecole polytechnique},
volume = {10},
doi = {10.5802/jep.223},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jep.223/}
}
TY - JOUR AU - Boutonnet, Rémi AU - Houdayer, Cyril TI - The noncommutative factor theorem for lattices in product groups JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 513 EP - 524 VL - 10 PB - Ecole polytechnique UR - https://www.numdam.org/articles/10.5802/jep.223/ DO - 10.5802/jep.223 LA - en ID - JEP_2023__10__513_0 ER -
%0 Journal Article %A Boutonnet, Rémi %A Houdayer, Cyril %T The noncommutative factor theorem for lattices in product groups %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 513-524 %V 10 %I Ecole polytechnique %U https://www.numdam.org/articles/10.5802/jep.223/ %R 10.5802/jep.223 %G en %F JEP_2023__10__513_0
Boutonnet, Rémi; Houdayer, Cyril. The noncommutative factor theorem for lattices in product groups. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 513-524. doi: 10.5802/jep.223
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