naa a22 4500 510782248 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0036-5 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0036-5 Generic representations of abelian groups and extreme amenability [Elektronische Daten] [Julien Melleray, Todor Tsankov] If G is a Polish group and Γ is a countable group, denote by Hom(Γ, G) the space of all homomorphisms Γ → G. We study properties of the group $$\overline {\pi (\Gamma )} $$ 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 space. Under mild assumptions on Γ, we prove that in the first case, there is (up to isomorphism of topological groups) a unique generic $$\overline {\pi (\Gamma )} $$ ; in the other two, we show that the generic $$\overline {\pi (\Gamma )} $$ is extremely amenable. We also show that if Γ is torsionfree, the centralizer of the generic π is as small as possible, extending a result of Chacon and Schwartzbauer from ergodic theory. Hebrew University Magnes Press, 2013 Melleray Julien CNRS UMR 5208 Université Lyon 1, Institut Camille Jordan, Université de Lyon, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne Cedex, France aut Tsankov Todor UFR de Mathématiques, case 7012 Institut de Mathématiques de Jussieu, Université Paris 7, 75205, Paris cedex 13, France aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 129-167 0021-2172 198:1<129 2013 198 11856 https://doi.org/10.1007/s11856-013-0036-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0036-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Melleray Julien CNRS UMR 5208 Université Lyon 1, Institut Camille Jordan, Université de Lyon, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne Cedex, France aut NATIONALLICENCE 700 1- Tsankov Todor UFR de Mathématiques, case 7012 Institut de Mathématiques de Jussieu, Université Paris 7, 75205, Paris cedex 13, France aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 129-167 0021-2172 198:1<129 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer