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• W3092096402 abstract "Let $ G $ be a countable discrete group and consider a nonsingular Bernoulli shift action $ G curvearrowright prod_{gin G }({0,1},mu_g)$ with two base points. When $ G $ is exact, under a certain finiteness assumption on the measures ${mu_g}_{gin G }$, we construct a boundary for the Bernoulli crossed product C$^*$-algebra that admits some commutativity and amenability in the sense of Ozawa's bi-exactness. As a consequence, we obtain that any such Bernoulli action is solid. This generalizes solidity of measure preserving Bernoulli actions by Ozawa and Chifan--Ioana, and is the first rigidity result in the non measure preserving case. For the proof, we use anti-symmetric Fock spaces and left creation operators to construct the boundary and therefore the assumption of having two base points is crucial." @default.
• W3092096402 created "2020-10-15" @default.
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• W3092096402 date "2021-06-11" @default.
• W3092096402 modified "2023-09-24" @default.
• W3092096402 title "Boundary and Rigidity of Nonsingular Bernoulli Actions" @default.
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• W3092096402 doi "https://doi.org/10.1007/s00220-021-04134-7" @default.
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