Property (T) for groups graded by root systems. Memoirs of the American Mathematical Society; volume 249, number 1186 (seventh of eight numbers).

Ershov, Mikhail; Jaikan-zapirain, Andrei; Kassabov, Martin

ISBN 10: 1470426048 / ISBN 13: 9781470426040

Published by Providence, American Mathematical Society, 2017

About this Item

Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00865 9781470426040 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2484704

Bibliographic Details

• Title: Property (T) for groups graded by root systems. Memoirs of the American Mathematical Society; volume 249, number 1186 (seventh of eight numbers).
• Publisher: Providence, American Mathematical Society
• Publication Date: 2017
• Language: English
• ISBN 10: 1470426048
• ISBN 13: 9781470426040
• Binding: Softcover
• Condition: Gut
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

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 $mathrm StPhi(R)$ and the elementary Chevalley group $mathbb EPhi(R)$ 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.

About the Author

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.