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
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