### A cancellative amenable ascending union of nonamenable semigroups

We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.

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We construct an example of a cancellative amenable semigroup which is the ascending union of semigroups, none of which are amenable.

In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if $G$ and $H$ are countable amenable non-type I groups, then the unitary duals of $G$ and $H$ are Borel isomorphic.

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let ${C}_{c}\left(G\right)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $({C}_{c}\left(G\right),{\epsilon}_{G})$ has property (FH) if and only if G has property (T). On...

The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...

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 $GL\left({V}_{\infty}\right)$, where ${V}_{\infty}$ is the countably infinite-dimensional...

We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.

This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.