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arXiv · 2105.06164

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

Alexandre I. Danilenko
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Abstract

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 amenable if and only if $G$ is amenable. If $G$ has the Haagerup property then (and only then) these actions can be chosen of 0-type. If $G$ is amenable and unimodular then $G$ has weakly mixing Bernoulli actions of any possible Krieger's type.

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Alexandre I. Danilenko. 2021-05-13. Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups. https://arxiv.org/abs/2105.06164

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