Eberlein oligomorphic groups
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- by Itaï Ben Yaacov, Tomás Ibarlucía and Todor Tsankov PDF
- Trans. Amer. Math. Soc. 370 (2018), 2181-2209 Request permission
Abstract:
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 $\aleph _0$-stable, $\aleph _0$-categorical structures. This analysis is then extended to all semitopological semigroup compactifications $S$ 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.References
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Additional Information
- Itaï Ben Yaacov
- Affiliation: Univ Lyon, Université Claude Bernard Lyon 1, Institut Camille Jordan, CNRS UMR 5208 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex France
- MR Author ID: 699648
- Tomás Ibarlucía
- Affiliation: Univ Lyon, Université Claude Bernard Lyon 1, Institut Camille Jordan, CNRS UMR 5208 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex France
- Address at time of publication: Institut de Mathématiques de Jussieu–PRG , Université Paris 7, case 7012 , 75205 Paris cedex 13 , France
- MR Author ID: 1161335
- Email: ibarlucia@math.univ-paris-diderot.fr
- Todor Tsankov
- Affiliation: Institut de Mathématiques de Jussieu–PRG , Université Paris 7, case 7012 , 75205 Paris cedex 13 , France
- MR Author ID: 781832
- Email: todor@math.univ-paris-diderot.fr
- Received by editor(s): January 8, 2017
- Published electronically: November 28, 2017
- Additional Notes: The authors were partially supported by the ANR contract GrupoLoco (ANR-11-JS01-0008). The second author was partially supported by the ANR contract ValCoMo (ANR-13-BS01-0006). The third author was partially supported by the ANR contract GAMME (ANR-14-CE25-0004).
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 2181-2209
- MSC (2010): Primary 22F50; Secondary 03C45, 22A25, 03C98, 22A15
- DOI: https://doi.org/10.1090/tran/7227
- MathSciNet review: 3739206