Comptes Rendus
no. 5
Lie algebras
On the structure and arithmeticity of lattice envelopes
[Sur la structure et l'arithméticité des groupes enveloppant un réseau]

Présenté par : the Editorial Board

Uri Bader1 ; Alex Furman2 ; Roman Sauer3
1 Technion, Haifa, Israel
2 University of Illinois at Chicago, Chicago, USA
3 Karlsruhe Institute of Technology, Karlsruhe, Germany
Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 409-413.

Nous nous intéressons à l'ensemble des plongements possibles d'un groupe dénombrable comme réseau dans un groupe localement compact. Pour une grande classe de groupes dénombrables, nous annonçons des résultats de structure et d'arithméticité de tels plongements. Cette classe contient tous les groupes linéaires dont l'adhérence de Zariski est simple, les groupes dont le premier nombre de Betti ℓ2 est non nul, les groupes hyperboliques acylindriques et les groupes de convergence.

We announce results about the structure and arithmeticity of all possible lattice embeddings of a class of countable groups that encompasses all linear groups with simple Zariski closure, all groups with non-vanishing first ℓ2-Betti number, non-elementary acylindrically hyperbolic groups, and non-elementary convergence groups.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.02.010
Uri Bader 1 ; Alex Furman 2 ; Roman Sauer 3

1 Technion, Haifa, Israel
2 University of Illinois at Chicago, Chicago, USA
3 Karlsruhe Institute of Technology, Karlsruhe, Germany 
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Uri Bader; Alex Furman; Roman Sauer. On the structure and arithmeticity of lattice envelopes. Comptes Rendus. Mathématique, Volume 353 (2015) no. 5, pp. 409-413. doi : 10.1016/j.crma.2015.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.02.010/

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Cité par Sources :

☆ This project was supported in part by ERC grant 306706 (U.B.), BSF grant 2008267 (U.B. and A.F.), and NSF grant DMS 1207803 (A.F.).

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