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arXiv · 2312.13153

Joining properties of automorphisms disjoint with all ergodic systems

Przemysław Berk·Martyna Górska·Thierry de la Rue
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Abstract

We study the class $Erg^\perp$ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of $Erg^\perp,$ that is, each automorphism whose every joining with an element of $Erg^{\perp}$ yields a system which is again an element of $Erg^{\perp}$, must be an identity. Despite this fact, we show that $Erg^\perp$ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in $Erg^\perp$ whose self-joinings always yield elements in $Erg^\perp$. This shows that there are non-trivial characteristic classes included in $Erg^\perp$.

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Przemysław Berk, Martyna Górska, Thierry de la Rue. 2023-12-20. Joining properties of automorphisms disjoint with all ergodic systems. https://arxiv.org/abs/2312.13153

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