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

Published online by Cambridge University Press:  06 June 2022

ALEXANDRE I. DANILENKO*
Affiliation:
B. Verkin Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences, 47 Nauky Ave., Kharkiv 61164, Ukraine

Abstract

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.

Type
Original Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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