Inventiones mathematicae

, 179:303

Property (T) for noncommutative universal lattices



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)

22D10 20F69 20E08 20E18 16S99 20E42 


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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

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