Eberlein oligomorphic groups
Résumé
We study the Fourier–Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups. We characterize the family of such groups whose Fourier–Stieltjes algebra is dense in the algebra of weakly almost periodic functions: those are exactly the automorphism groups of ℵ 0-stable, ℵ 0-categorical structures. This analysis is then extended to all semitopological semigroup compactifica-tions S of such a group: S is Hilbert-representable if and only if it is an inverse semigroup. We also show that every factor of the Hilbert compactification is Hilbert-representable.
| Origine | Fichiers produits par l'(les) auteur(s) |
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