English

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

Dynamical Systems 2022-06-14 v2

Abstract

It is shown that each non-compact locally compact second countable non-(T) group GG possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger's type. These actions are amenable if and only if GG is amenable. If GG has the Haagerup property then (and only then) these actions can be chosen of 0-type. If GG is amenable and unimodular then GG has weakly mixing Bernoulli actions of any possible Krieger's type.

Keywords

Cite

@article{arxiv.2105.06164,
  title  = {Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups},
  author = {Alexandre I. Danilenko},
  journal= {arXiv preprint arXiv:2105.06164},
  year   = {2022}
}

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Slightly modified version