Hilbert C*-systems for actions of the circle group

Abstract

The paper contains constructions of Hilbert systems for the action of the circle group $T$ using subgroups of implementable Bogoljubov unitaries w.r.t. Fock representations of the Fermion algebra for suitable data of the selfdual framework: $\mathcal{H}$ is the reference Hilbert space, $\Gamma$ the conjugation and $P$ a basis projection on $\mathcal{H}.$ The group $C(spec\mathcal{Z}\to T)$ of $T$-valued functions on $spec\mathcal{Z}$ turns out to be isomorphic to the stabilizer of $\mathcal{A}$. In particular, examples are presented where the center $\mathcal{Z}$ of the fixed point algebra $\mathcal{A}$ can be calculated explicitly.

14 pages, Latex

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