More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

TL;DR

This paper computes universal minimal flows for automorphism groups of various uncountable homogeneous structures, expanding the class of known extremely amenable groups and providing a straightforward construction method.

Contribution

It introduces a simple construction for uncountable homogeneous structures and determines their automorphism groups' universal minimal flows, broadening the understanding of extremely amenable groups.

Findings

Computed universal minimal flows for automorphism groups of uncountable structures

Provided a new easy construction method for these structures

Expanded the class of known extremely amenable groups

Abstract

In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions with an $\omega$-homogeneous ordering. We present an easy construction of such structures, expanding the jungle of extremely amenable groups.