Eberlein oligomorphic groups

2016/02/16 by Yaacov, Itaï Ben, Ibarlucía, Tomás, Tsankov, Todor · 2 citations
#22F50 #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1602.05097

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 ℵ₀-stable, ℵ₀-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.

Cited by

• Enveloping semigroups as compactifications of topological groups
• On two methods of constructing compactifications of topological groups

Related

• Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups
• Compactification of bounded semigroup representations
• The group \Aut(μ) is Roelcke precompact
• On operator amenability of Fourier-Stieltjes algebras
• Property (T) for Roelcke precompact Polish groups (after Ibarlucía, building on work of Ben Yaacov and Tsankov)