Krieger's type of nonsingular Poisson suspensions and IDPFT systems

Abstract

Given an infinite countable discrete amenable group $\Gamma$, we construct explicitly sharply weak mixing nonsingular Poisson $\Gamma$-actions of each Krieger's type: $II{I}_{\lambda }$, for $\lambda \in [0,1]$, and $I{I}_{\infty }$. The result is new even for $\Gamma =\mathbb{Z}$. 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.

arXiv commentCorrected, more detailed version