Right $\mathrm{\ell }$-groups associated with von Neumann algebras

In [Rum18], Rump defined and characterized noncommutative universal groups $G(X)$ for generalized orthomodular lattices $X$. We give an explicit construction of $G(X)$ in terms of \emph{pure paraunitary groups} when $X$ is the projection lattice of a von Neumann algebra. The results given here extend some of those in [Die19].