A characterization of relative Kazhdan Property T for semidirect products with abelian groups

Details A characterization of relative Kazhdan Property T for semidirect products with abelian groups A characterization of relative Kazhdan Property T for semidirect products with abelian groups

2009-11-17

arxiv.org/abs/0911.3371v3

Ergod. Th. & Dynam. Sys. (2011), 31, 793-805

Mathematics

Group Theory

16 pages, no figure. v1->v2: The main result has been slightly restated because of a flaw in the original argument v2->v3 adde

Scientific paper

10.1017/S0143385710000271

Let A be a locally compact abelian group, and H a locally compact group
acting on A. Let G=HA be the semidirect product. We prove that the pair (G,A)
has Kazhdan's Property T if and only if the only countably approximable
H-invariant mean on the Borel subsets of the Pontryagin dual of A, supported at
the neighbourhood of the trivial character, is the Dirac measure.

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