期刊
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
卷 370, 期 3, 页码 2181-2209出版社
AMER MATHEMATICAL SOC
DOI: 10.1090/tran/7227
关键词
Hilbert compactification; oligomorphic; No-categorical; Fourier Stieltjes algebra; semitopological semigroup compactification; inverse semigroup; Hilbert representable
类别
资金
- ANR contract GrupoLoco [ANR-11-JS01-0008]
- ANR contract ValCoMo [ANR-13-BS01-0006]
- ANR contract GAMME [ANR-14-CE25-0004]
- Agence Nationale de la Recherche (ANR) [ANR-14-CE25-0004, ANR-11-JS01-0008, ANR-13-BS01-0006] Funding Source: Agence Nationale de la Recherche (ANR)
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 No-stable, No-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.
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