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: $III_\lambda$, 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.00405
 Bibcode:
 2020arXiv201000405D
 Keywords:

 Mathematics  Dynamical Systems;
 37A40
 EPrint:
 Corrected, more detailed version