On Relative Property (T) and Haagerup's Property

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

2009-06-29

arxiv.org/abs/0906.5363v1

Mathematics

Group Theory

Scientific paper

We consider the following three properties for countable discrete groups $\Gamma$: (1) $\Gamma$ has an infinite subgroup with relative property (T), (2) the group von Neumann algebra $L\Gamma$ has a diffuse von Neumann subalgebra with relative property (T) and (3) $\Gamma$ does not have Haagerup's property. It is clear that (1) $\Longrightarrow$ (2) $\Longrightarrow$ (3). We prove that both of the converses are false.

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