BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW

Author:

Berendschot TeyORCID,Vaes StefaanORCID

Abstract

AbstractWe prove that many, but not all, injective factors arise as crossed products by nonsingular Bernoulli actions of the group$\mathbb {Z}$. We obtain this result by proving a completely general result on the ergodicity, type and Krieger’s associated flow for Bernoulli shifts with arbitrary base spaces. We prove that the associated flow must satisfy a structural property of infinite divisibility. Conversely, we prove that all almost periodic flows, as well as many other ergodic flows, do arise as associated flow of a weakly mixing Bernoulli action of any infinite amenable group. As a byproduct, we prove that all injective factors with almost periodic flow of weights are infinite tensor products of$2 \times 2$matrices. Finally, we construct Poisson suspension actions with prescribed associated flow for any locally compact second countable group that does not have property (T).

Funder

Vlaamse regering

Fonds Wetenschappelijk Onderzoek

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Ergodic Theory: Nonsingular Transformations;Encyclopedia of Complexity and Systems Science Series;2023

2. Ergodic Theory: Nonsingular Transformations;Encyclopedia of Complexity and Systems Science;2022

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