Superselection structures for C*-algebras with nontrivial center

Abstract

We present and prove some results within the framework of Hilbert C*-systems $\{{\cal F},{\cal G}\}$ with a compact group ${\cal G}$. We assume that the fixed point algebra ${\cal A}\subset{\cal F}$ of ${\cal G}$ has a nontrivial center ${\cal Z}$ and its relative commutant w.r.t. ${\cal F}$ coincides with ${\cal Z}$, i.e., we have ${\cal A}'\cap{\cal F}= {\cal Z}\supset\bbfC\text{\bf 1}$. In this context, we propose a generalization of the notion of an irreducible endomorphism and study the behaviour of such irreducibles w.r.t. ${\cal Z}$. Finally, we give several characterizations of the stabilizer of ${\cal A}$.