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arXiv · 0809.4095

Property $(T)$ for noncommutative universal lattices

Mikhail Ershov·Andrei Jaikin-Zapirain
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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 $EL_n(R)$, where $n\geq 3$ 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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Mikhail Ershov, Andrei Jaikin-Zapirain. 2009-12-21. Property $(T)$ for noncommutative universal lattices. https://doi.org/10.1007/s00222-009-0218-2

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