TY - JOUR
T1 - KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS
AU - Danilenko, Alexandre I.
AU - Kosloff, Zemer
N1 - Publisher Copyright:
© 2022 American Mathematical Society
PY - 2022
Y1 - 2022
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.
UR - http://www.scopus.com/inward/record.url?scp=85124604936&partnerID=8YFLogxK
U2 - 10.1090/proc/15695
DO - 10.1090/proc/15695
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AN - SCOPUS:85124604936
SN - 0002-9939
VL - 150
SP - 1541
EP - 1557
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -