Bernoulli actions of amenable groups with weakly mixing Maharam extensions

Abstract

We provide a simple criterion for a non-singular and conservative Bernouilli action to have a weakly mixing Maharam extension. As an application, we show that every countable amenable group admits a stable type III_1 Bernoulli action, answering a recent question by Vaes and Wahl.

Proposition 1.7 in the old version, which was based on an incorrect criterion for determining essential values contained in Lemma 2.1 in the paper "Abelian cocycles for non-singular ergodic transformations and the genericity of type III transformations", has been corrected

Cited by in corpus (3)

• Nonsingular Bernoulli actions of arbitrary Krieger type
• Bernoulli actions of type III${}_0$ with prescribed associated flow
• Symmetric Stable Processes on Amenable Groups