Publication:
Superselection structures for C*-algebras with nontrivial center

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ISSN: 0129-055X (Print)
ISSN: 1793-6659 (Online)
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1997
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World Scientific Publishing
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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 ${\cal A}$.
Description
35 pages, no figures.-- MSC2000 codes: 46L05, 46L60.
MR#: MR1475657 (99g:46097)
Zbl#: Zbl 0893.46046
Keywords
Hilbert C*-systems, Compact group, Nontrivial center, Relative commutant, Irreducible endomorphism, Characterizations of the stabilizer
Bibliographic citation
Reviews in Mathematical Physics, 1997, vol. 9, n. 7, p. 785-819