Spectra of ergodic transformations

We study the group properties of the spectrum of a strongly continuous unitary representation of a locally compact Abelian group G implementing an ergodic group of ¹-automorphisms of a von Neumann algebra $\text{R}$. It is shown that in many cases the spectrum equals the dual group of G; e.g. if G is the integers and $\text{R}$ not finite dimensional and Abelian, then the spectrum is the circle group.