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nonsingular poisson action

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Krieger’s type for ergodic non-singular Poisson actions of non-(T) locally compact groups
Part of
- Ergodic theory
ALEXANDRE I. DANILENKO
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 7 / July 2023

Published online by Cambridge University Press:

06 June 2022, pp. 2317-2353

Print publication:

July 2023
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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.