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Hilbert C*-systems for actions of the circle group

H. Baumgaertel·A. L. Carey
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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: ${\cal H}$ is the reference Hilbert space, $Γ$ the conjugation and $P$ a basis projection on ${\cal H}.$ The group $C({spec} {\cal Z}\to T)$ of $T$-valued functions on ${spec} {\cal Z}$ turns out to be isomorphic to the stabilizer of ${\cal A}$. In particular, examples are presented where the center ${\cal Z}$ of the fixed point algebra ${\cal A}$ can be calculated explicitly.

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H. Baumgaertel, A. L. Carey. 2000-10-10. Hilbert C*-systems for actions of the circle group. https://doi.org/10.1016/s0034-4877(01)80048-3

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