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

Abstract

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.

16 pages, no figure. v1->v2: The main result has been slightly restated because of a flaw in the original argument v2->v3 added Theorem 4 which provides a relative version

References in corpus (1)

• On Relative Property (T) and Haagerup's Property

Cited by in corpus (3)

• Locally compact wreath products
• Quasi-homomorphism rigidity with noncommutative targets
• Rigidity for group actions on homogeneous spaces by affine transformations