Representations of Nets of C-*-Algebras over S (1)

In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C-*-algebras over S (1) admits faithful representations, and when the net is covariant under Diff(S (1)), it admits representations covariant under any amenable subgroup of Diff(S (1)).