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: H is the reference Hilbert space, the conjugation and P a basis projection on H: According to a general result for Hilbert systems of this type, the group C(spec Z ! T ) of T -valued functions on spec Z is isomorphic to the stabilizer of A. In particular, examples are presented where the center Z of the xed point algebra A can be calculated explicitly
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