Year: 2024
Type: article
Abstract: We study the class $\operatorname {Erg}^\perp $ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of $\operatorname {Erg}^\perp ,$ that is, each automorphism whose every joining with an element of $\operatorname {Erg}^{\perp }$ yields a system which is again an element of $\operatorname {Erg}^{\perp }$ , must be an identity. Despite this fact, we show that $\operatorname {Erg}^\perp $ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in $\operatorname {Erg}^\perp $ whose self-joinings always yield elements in $\operatorname {Erg}^\perp $ . This shows that there are non-trivial characteristic classes included in $\operatorname {Erg}^\perp $ .
Authors: PRZEMYSŁAW BERK, MARTYNA GÓRSKA, THIERRY DE LA RUE
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4405850654