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

Part of: Ergodic theory

Published online by Cambridge University Press:  06 June 2022

ALEXANDRE I. DANILENKO Open the ORCID record for ALEXANDRE I. DANILENKO [Opens in a new window]
ALEXANDRE I. DANILENKO*
Affiliation:
B. Verkin Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences, 47 Nauky Ave., Kharkiv 61164, Ukraine
*
e-mail: [email protected]
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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.

Keywords

Nonsingular Poisson actionKrieger typeKazhdan property (T)Haagerup propertyamenable action

MSC classification

Primary: 37A40: Nonsingular (and infinite-measure preserving) transformations
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 7 , July 2023 , pp. 2317 - 2353
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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