The algebraization of Kazhdan’s property (T)
نویسنده
چکیده
We present the surge of activity since 2005, around what we call the algebraic (as contrasted with the geometric) approach to Kazhdan’s property (T). The discussion includes also an announcement of a recent result (March 2006) regarding property (T) for linear groups over arbitrary finitely generated rings.
منابع مشابه
Group Actions on Median Spaces
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan’s property (T) and Haagerup’s property.
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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 [DJ].
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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 [DJ].
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Kazhdan’s property T has recently been imported to the C∗-world by Bekka. Our objective is to extend a well known fact to this realm; we show that a nuclear C∗-algebra with property T is finite dimensional (for all intents and purposes). Though the result is not surprising, the proof is a bit more complicated than the group case.
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