KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

Alexandre I. Danilenko; Zemer Kosloff

doi:10.1090/proc/15695

KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

Alexandre I. Danilenko, Zemer Kosloff

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: III_λ, for λ ∈ [0, 1], and II_∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

Original language	American English
Pages (from-to)	1541-1557
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
DOIs	https://doi.org/10.1090/proc/15695
State	Published - Apr 2022

Bibliographical note

Funding Information:
Received by the editors October 1, 2020, and, in revised form, May 30, 2021, and June 7, 2021. 2020 Mathematics Subject Classification. Primary 37A40. The second author was partially supported by ISF grant No. 1570/17.

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© 2022 American Mathematical Society

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title = "KRIEGER{\textquoteright}S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS",

abstract = "Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger{\textquoteright}s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger{\textquoteright}s type.",

author = "Danilenko, {Alexandre I.} and Zemer Kosloff",

note = "Funding Information: Received by the editors October 1, 2020, and, in revised form, May 30, 2021, and June 7, 2021. 2020 Mathematics Subject Classification. Primary 37A40. The second author was partially supported by ISF grant No. 1570/17. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

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AU - Danilenko, Alexandre I.

AU - Kosloff, Zemer

N1 - Funding Information: Received by the editors October 1, 2020, and, in revised form, May 30, 2021, and June 7, 2021. 2020 Mathematics Subject Classification. Primary 37A40. The second author was partially supported by ISF grant No. 1570/17. Publisher Copyright: © 2022 American Mathematical Society

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N2 - Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

AB - Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

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ER -

KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

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