title: Groups graded by root systems and property (T).
abstract: We establish property (T) for a large class of groups graded by root systems, including elementary Chevalley groups and Steinberg groups of rank at least 2 over finitely generated commutative rings with 1. We also construct a group with property (T) which surjects onto all finite simple groups of Lie type and rank at least two.
authors.affiliation: Department of Mathematics, University of Virginia, Charlottesville, VA 22904; ershov@virginia.edu.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Ershov
authors.affiliation: Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas, Spanish National Research Council-Universidad Autónoma de Madrid-Universidad Carlos III de Madrid-Universidad Complutense de Madrid, Madrid 28049, Spain;
authors.forename: Andrei
authors.initials: A
authors.lastname: Jaikin-Zapirain
authors.affiliation: Department of Mathematics, Cornell University, Ithaca, NY 14853; and.
authors.forename: Martin
authors.initials: M
authors.lastname: Kassabov
authors.affiliation: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093.
authors.forename: Zezhou
authors.initials: Z
authors.lastname: Zhang
keywords: Chevalley groups; Steinberg groups; property (T); root system gradings