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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2014 | 226 | 1 | 41-61

## Amenability and unique ergodicity of automorphism groups of Fraïssé structures

EN

### Abstrakty

EN
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.

41-61

wydano
2014

### Twórcy

autor
• Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.