Krieger’s type of nonsingular Poisson suspensions and IDPFT systems

DOI10.1090/proc/15695zbMath1490.37008arXiv2010.00405OpenAlexW3166596799MaRDI QIDQ5027196

Zemer Kosloff, Alexandre I. Danilenko

Publication date: 4 February 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00405

zbMATH Keywords

discrete amenable groupBernoulli \(\Gamma\)-actionsPoisson \(\Gamma\)-actions

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Nonsingular (and infinite-measure preserving) transformations (37A40)

Related Items (4)

Haagerup property and Kazhdan pairs via ergodic infinite measure preserving actions ⋮ Krieger’s type for ergodic non-singular Poisson actions of non-(T) locally compact groups ⋮ BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW ⋮ Generic non-singular Poisson suspension is of type III₁

Cites Work

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• Abelian cocycles for nonsingular ergodic transformations and the genericity of type \(III_ 1\) transformations
• Entropy and isomorphism theorems for actions of amenable groups
• Absolute continuity of Poisson random fields
• Bernoulli actions of type \(\mathrm{III}_{1}\) and \(L^2\)-cohomology
• The orbital equivalence of Bernoulli actions and their Sinai factors
• Nonsingular Bernoulli actions of arbitrary Krieger type
• Nonsingular Poisson suspensions
• Mildly Mixing Actions of Locally Compact Groups
• Conditioning as disintegration
• σ-Finite Invariant Measures on Infinite Product Spaces

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