• DOI:10.1007/s00220-021-04134-7
• Corpus ID: 222177045

Boundary and Rigidity of Nonsingular Bernoulli Actions

@article{Hasegawa2020BoundaryAR,
  title={Boundary and Rigidity of Nonsingular Bernoulli Actions},
  author={K. Hasegawa and Yusuke Isono and Tomohiro Kanda},
  journal={Communications in Mathematical Physics},
  year={2020},
  volume={389},
  pages={977 - 1008}
}

• K. Hasegawa, Yusuke Isono, T. Kanda
• Published 7 October 2020
• Mathematics
• Communications in Mathematical Physics

Let G be a countable discrete group and consider a nonsingular Bernoulli shift action G↷∏g∈G({0,1},μg)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ G \curvearrowright \prod _{g\in G }(\{0,1\},\mu _g)$$\end{document} with 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.