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1 results

Orbit equivalence superrigidity for type III$_0$ actions
Part of
- Ergodic theory
- Selfadjoint operator algebras
STEFAAN VAES, BRAM VERJANS
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 12 / December 2023

Published online by Cambridge University Press:

13 December 2022, pp. 4193-4225

Print publication:

December 2023
- Article
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We prove the first orbit equivalence superrigidity results for actions of type III$_\unicode{x3bb} $ when $\unicode{x3bb} \neq 1$. These actions arise as skew products of actions of dense subgroups of $\operatorname {SL}(n,\mathbb {R})$ on the sphere $S^{n-1}$ and they can have any prescribed associated flow.