Inventiones mathematicae

, 179:303

Property (T) for noncommutative universal lattices


DOI: 10.1007/s00222-009-0218-2

Cite this article as:
Ershov, M. & Jaikin-Zapirain, A. Invent. math. (2010) 179: 303. doi:10.1007/s00222-009-0218-2


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 (Dymara and Januszkiewicz in Invent. Math. 150(3):579–627, 2002).

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.University of VirginiaCharlottesvilleUSA
  2. 2.Departamento de Matematicas UAMInstituto de Ciencias Matematicas CSIC-UAM-UC3M-UCMMadridSpain