For finitely generated nilpotent groups, left and right ℓ²-Dirichlet structures coincide if and only if the group is virtually abelian, via skewed Følner geometry and left schemes; this yields first asymmetric Bernoulli schemes over amenable groups.
Bernoulli actions of amenable groups with weakly mixing
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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.
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Asymmetry of $\ell^{2}$-cohomology via skewed F{\o}lner geometry
For finitely generated nilpotent groups, left and right ℓ²-Dirichlet structures coincide if and only if the group is virtually abelian, via skewed Følner geometry and left schemes; this yields first asymmetric Bernoulli schemes over amenable groups.