Amenability and unique ergodicity of automorphism groups of Fraïssé structures

• Autorzy: Andy Zucker
• Języki publikacji: 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.

Kategorie tematyczne

• 22F50: Groups as automorphisms of other structures
• 54H20: Topological dynamics
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 03E02: Partition relations
• 22F10: Measurable group actions
• 05D10: Ramsey theory
• 03E15: Descriptive set theory
• 03C15: Denumerable structures
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 1
• Strony: 41-61

Daty

wydano

2014

Twórcy

autor

Andy Zucker

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

Identyfikatory

DOI

10.4064/fm226-1-3