# Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

@article{Danilenko2020KriegersTO, title={Krieger’s type of nonsingular Poisson suspensions and IDPFT systems}, author={Alexandre I. Danilenko and Zemer Kosloff}, journal={arXiv: Dynamical Systems}, year={2020} }

Given an infinite countable discrete amenable group $\Gamma$, we construct explicitly sharply weak mixing nonsingular Poisson $\Gamma$-actions of each Krieger's type: $III_\lambda$, for $\lambda\in[0,1]$, and $II_\infty$. The result is new even for $\Gamma=\Bbb Z$. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli $\Gamma$-actions and IDPFT systems of each possible Krieger's type.

## 3 Citations

Bernoulli actions of type III$_0$ with prescribed associated flow

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We prove that many, but not all injective factors arise as crossed products by nonsingular Bernoulli actions of the group Z. We obtain this result by proving a completely general result on the…

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It is shown that a locally compact second countable group G has the Haagerup property if and only if there exists a sharply weak mixing 0-type measure preserving free G-action T = (Tg)g∈G on an…

Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups

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It is shown that each non-compact locally compact second countable non-(T) group G possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger’s type. These actions are…

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