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Bernoulli actions of type III_1 and L^2-cohomology. (arXiv:1705.00439v3 [math.DS] UPDATED)
来源于:arXiv
We conjecture that a countable group $G$ admits a nonsingular Bernoulli
action of type III$_1$ if and only if the first $L^2$-cohomology of $G$ is
nonzero. We prove this conjecture for all groups that admit at least one
element of infinite order. We also give numerous explicit examples of type
III$_1$ Bernoulli actions of the group of integers and the free groups, with
different degrees of ergodicity. 查看全文>>