Property ($T$) for Groups Graded by Root Systems (Memoirs of the American Mathematical Society) - Softcover

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

Softcover

ISBN 10: 1470426048 ISBN 13: 9781470426040

Verlag: American Mathematical Society, 2017

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2017
• Sprache: Englisch
• ISBN 10: 1470426048
• ISBN 13: 9781470426040
• Einband: Tapa blanda
• Anzahl der Seiten: 135
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar