Property (T) for noncommutative universal lattices
Abstract
We establish a new spectral criterion for Kazhdan's property (T) which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property (T) for the groups ELn(R), where n≥ 3 and R is an arbitrary finitely generated associative ring. We also strengthen some of the results on property (T) for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).
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