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Article . 1969
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American Journal of Mathematics
Article . 1969 . Peer-reviewed
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The Dual Space of Semi-Simple Lie Groups

The dual space of semi-simple Lie groups
Authors: Wang, S. P.;

The Dual Space of Semi-Simple Lie Groups

Abstract

Introduction. This paper is inspired by Kazhdan's work [8]. In [8], he has studied the structure of lattices, i.e., discrete subgroups with finite invariant measure on the factor space, of a Lie group by investigating a particular topological property of the dual space of a Lie group. Let G be a separable locally compact group and G its dual space. G is said to have property (T) if the class of the trivial representation2 is an isolated point in G. In [8], it is proved that if G has property (T), then any lattice P of G also has property (T) ; in particular, by [8, Theorem 2], P is finitely generated and r/[Jr, r] is finite. Kazhdan has proved that connected simple Lie groups with finite center and R-rank > 2 have property (T) based on his study of SL(3,R). Here by the same approach, we show that SO(2,3) has property (T). Thus we are able to conclude the following theorem:

Keywords

group theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
26
Average
Top 10%
Average
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