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Groups graded by root systems and property (T)
Mikhail Ershov1, Andrei Jaikin-Zapirain2, Martin Kassabov3
1Department of Mathematics, University of Virginia, Charlottesville, VA 22904; ershov@virginia.edu.
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.
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