Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

Alexandre Danilenko; Zemer Kosloff

doi:10.1090/proc/15695

Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

Alexandre Danilenko, Zemer Kosloff

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

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 nonsingularBernoulli Γ-actions and infinite direct product of finite type systems of each
possible Krieger’s type.

Original language	English
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
DOIs	https://doi.org/10.1090/proc/15695
Publication status	Published - 13 Jan 2022

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title = "Krieger{\textquoteright}s type of nonsingular Poisson suspensions and IDPFT systems",

abstract = "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 nonsingularBernoulli Γ-actions and infinite direct product of finite type systems of eachpossible Krieger{\textquoteright}s type.",

author = "Alexandre Danilenko and Zemer Kosloff",

year = "2022",

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day = "13",

doi = "10.1090/proc/15695",

language = "English",

volume = "150",

journal = "Proceedings of the American Mathematical Society",

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T1 - Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

AU - Danilenko, Alexandre

AU - Kosloff, Zemer

PY - 2022/1/13

Y1 - 2022/1/13

N2 - Abstract. 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 nonsingularBernoulli Γ-actions and infinite direct product of finite type systems of eachpossible Krieger’s type.

AB - Abstract. 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 nonsingularBernoulli Γ-actions and infinite direct product of finite type systems of eachpossible Krieger’s type.

U2 - 10.1090/proc/15695

DO - 10.1090/proc/15695

M3 - Article (Academic Journal)

SN - 0002-9939

VL - 150

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

Abstract

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