Property $t$ for Groups Graded by Root Systems - Couverture souple

Ershov, Mikhail; Jaikin-Zapirain, Andrei; Kassabov, Martin

Couverture souple

ISBN 10 : 1470426048 ISBN 13 : 9781470426040

Editeur : American Mathematical Society, 2017

Synopsis

The authors introduce and study the class of groups graded by root systems. They prove that if $\Phi$ is an irreducible classical root system of rank $\geq 2$ and $G$ is a group graded by $\Phi$, then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of $G$. As the main application of this theorem the authors prove that for any reduced irreducible classical root system $\Phi$ of rank $\geq 2$ and a finitely generated commutative ring $R$ with $1$, the Steinberg group ${\mathrm St}_{\Phi}(R)$ and the elementary Chevalley group $\mathbb E_{\Phi}(R)$ have property $(T)$. They also show that there exists a group with property $(T)$ which maps onto all finite simple groups of Lie type and rank $\geq 2$, thereby providing a ``unified'' proof of expansion in these groups.

A propos du livre

À propos de l?auteur

Mikhail Ershov, University of Virginia, Charlottesville, Virginia.

Andrei Jaikin-Zapirain, Universidad Autonoma de Madrid, Spain and Instituto de Ciencias Matematicas, Madrid, Spain.

Martin Kassabov, Cornell University, Ithaca, New York, and University of Southampton, United Kingdom.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2017
• Langue: anglais
• ISBN 10: 1470426048
• ISBN 13: 9781470426040
• Reliure: Broché
• Nombre de pages: 135
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible