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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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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