Noncommutative joinings II

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