Amenability and unique ergodicity of automorphism groups of Fraïssé structures

Andy Zucker

Andy Zucker

Fundamenta Mathematicae, Tome 227 (2014), p. 41-61 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering $G L (V_{\infty})$ , where $V_{\infty}$ is the countably infinite-dimensional vector space over a finite field $F_{q}$ , we show that the unique invariant measure on the universal minimal flow of $G L (V_{\infty})$ is not supported on the generic orbit.

Publié le : 2014-01-01

Zbl 06296424

EUDML-ID : urn:eudml:doc:286626

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     author = {Andy Zucker},
     title = {Amenability and unique ergodicity of automorphism groups of Fra\"\i ss\'e structures},
     journal = {Fundamenta Mathematicae},
     volume = {227},
     year = {2014},
     pages = {41-61},
     zbl = {06296424},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-1-3}
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Andy Zucker. Amenability and unique ergodicity of automorphism groups of Fraïssé structures. Fundamenta Mathematicae, Tome 227 (2014) pp. 41-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-1-3/