Automorphism groups of generic structures: extreme amenability and amenability
نویسندگان
چکیده
منابع مشابه
Generic representations of abelian groups and extreme amenability
If G is a Polish group and Γ is a countable group, denote byHom(Γ,G) the space of all homomorphisms Γ → G. We study properties of the group π(Γ) for the generic π ∈ Hom(Γ,G), when Γ is abelian and G is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and the isometry group of the Urysohn metric...
متن کاملExtreme Amenability of Abelian
We show that for any abelian topological group G and arbitrary diffused submeasure μ, every continuous action of L0(μ,G) on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and Weiss, and Farah and Solecki. This also answers a question posed by Farah and Solecki. In particular, it implies that if H is of the form L0(μ,R), then H ...
متن کاملExtreme Amenability of L0, a Ramsey Theorem, and Lévy Groups
We show that L0(φ, H) is extremely amenable for any diffused submeasure φ and any solvable compact group H. This extends results of Herer–Christensen and of Glasner and Furstenberg–Weiss. Proofs of these earlier results used spectral theory or concentration of measure. Our argument is based on a new Ramsey theorem proved using ideas coming from combinatorial applications of algebraic topologica...
متن کاملWeak amenability of Coxeter groups
Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g 7→ rl(g). (Here 0 < r < 1, and l denotes the length function with respect to the generating set S.) The constructed representations are uniformly bounded and we prove that this implies the weak amenability of the group G. Résumé Soit (G...
متن کاملWeak Amenability of Hyperbolic Groups
We prove that hyperbolic groups are weakly amenable. This partially extends the result of Cowling and Haagerup showing that lattices in simple Lie groups of real rank one are weakly amenable. We take a combinatorial approach in the spirit of Haagerup and prove that for the word length metric d on a hyperbolic group, the Schur multipliers associated with r have uniformly bounded norms for 0 < r ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2018
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm435-10-2017