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

It is shown that each locally compact second countable non-(T) group G admits non-strongly ergodic weakly mixing IDPFT Poisson actions of any possible Krieger 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 chos...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2023-07, Vol.43 (7), p.2317-2353
Main Author: DANILENKO, ALEXANDRE I.
Format: Article
Language:English
Subjects:
Ergodic processes
Original Article
Theorems
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Summary:It is shown that each locally compact second countable non-(T) group G admits non-strongly ergodic weakly mixing IDPFT Poisson actions of any possible Krieger 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, then G admits weakly mixing Bernoulli actions of arbitrary Krieger type.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2022.34