Hilbert C*-Systems for Actions of the Circle Group

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, Γ the conjugation and P a basis projection on H. The group C(spec Z → T) of T-valued functions on spec Z turns out to be isomorphic to the stabilizer of A. In particular, examples are presented where the center Z of the fixed point algebra A can be calculated explicitly.