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arXiv · 1905.06725

Noncommutative Joinings II

Jon Bannon·Jan Cameron·Kunal Mukherjee
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Abstract

This paper is a continuation of the authors' previous work on noncommutative joinings, and contains a study of relative independence of W$^*$-dynamical systems. We prove that, given any separable locally compact group $G$, an ergodic W$^{*}$-dynamical $G$-system $\mathfrak{M}$ with compact subsystem $\mathfrak{N}$ is disjoint relative to $\mathfrak{N}$ from its maximal compact subsystem $\mathfrak{M}_{K}$ if and only if $\mathfrak{N}\cong\mathfrak{M}_{K}$. This generalizes recent work of Duvenhage, which established the result for $G$ abelian.

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Jon Bannon, Jan Cameron, Kunal Mukherjee. 2019-05-16. Noncommutative Joinings II. https://arxiv.org/abs/1905.06725

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