Boundary and Rigidity of Nonsingular Bernoulli Actions
Boundary and Rigidity of Nonsingular Bernoulli Actions
复制标题
非奇异伯努利作用的边界和刚性
DOI：
10.1007/s00220-021-04134-7
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发表时间：
2022
影响因子：
2.4
通讯作者：
Kanda Tomohiro
中科院分区：
文献类型：
--
作者：
Hasegawa Kei;Isono Yusuke;Kanda Tomohiro
设G是一个可数离散群，考虑具有两个基点的非奇异Bernoulli移位作用。利用非奇异Bernoulli作用的一个新边界，证明了某些非奇异Bernoulli作用的固定性，从而证明了非保测度Bernoulli位移作用的第一个刚性结果。这推广了Ozawa和Chifan-Ioana的保持Bernoulli作用的测度的固定性。为了证明，我们使用反对称Fock空间和左创建算子来构造边界，因此具有两个基点的假设是至关重要的。
LetGbe a countable discrete group and consider a nonsingular Bernoulli shift actionwith two base points. We prove the first rigidity result for Bernoulli shift actions that are not measure preserving, by proving solidity for certain non-singular Bernoulli actions, making use of a new boundary associated with such Bernoulli actions. This generalizes solidity of measure preserving Bernoulli actions by Ozawa and Chifan–Ioana. 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.