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Amenability and unique ergodicity of automorphism groups of Fraïssé structures

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Zucker A.

Fundamenta Mathematicae

2014

tom 226

nr 1

41-61

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 $GL(V_{∞})$, where $V_{∞}$ 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 $GL(V_{∞})$ is not supported on the generic orbit.

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1 Fundamenta Mathematicae

1 Zucker A.

1 2014

Wyniki wyszukiwania

Amenability and unique ergodicity of automorphism groups of Fraïssé structures