Related papers: Amenability of Universal 2-Grigorchuk group

We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely…

The aim of this brief note is to offer another proof of a theorem of Hrushovski that approximate subgroups of GL_n(C) are almost nilpotent. This approach generalizes to uniformly non amenable groups.

We classify all finite 2-groups that have a cyclic or dihedral maximal subgroup and determine their automorphism groups. Based on this result, we classify all pairs $ (G,\mathcal{M}) $, such that $ G $ is a finite 2-group and $ \mathcal{M}…

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups…

We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…

Every finite simple group can be generated by two elements, and in 2000, Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group every nontrivial element belongs to a generating pair. Groups with…

We provide a new characterization of amenability for countable groups, based on frame representations admitting almost invariant vectors. By relaxing the frame inequalities, thereby weakening amenability, we obtain a large class of…

Let $K$ be a spherically complete field with a non-Archimedean valuation. We define a new version of $K-$amenability for discrete groups and show that the Banach $K-$algebra $l^1(G)$ is amenable iff $G$ is $K-$amenable in our sense.

Let G be one of the local gauge groups C(X,U(n)), C^\infty(X,U(n)), C(X,SU(n)) or C^\infty(X,SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which…

We show that for any full and sufficiently transitive (i.e. \textit{flexible}) group $G$ of homeomorphisms of Cantor space, $\mathrm{Aut}(\mathrm{Aut}(G)) = \mathrm{Aut}(G)$. This class contains many generalisations of the Higman-Thompson…

Averaging linear functional on the space continuous functions of the group of diffeomorphisms of interval is found. Amenability of several discrete subgroups of the group of diffeomorphisms $\Diff^3([0,1])$ of interval is prove. In…

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set…

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

We show that the class of amalgamated free products of two free groups over a cyclic subgroup admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

We show that for any countable amenable group action, along F{\o}lner sequences that have for any $c>1$ a two sided $c$-tempered tail, one have universal estimate for the probability that there are $n$ fluctuations in the ergodic averages…

As a consequence of Kirchberg's work, Connes' Embedding Conjecture is equivalent to the property that every homomorphism of the group $F_\infty\times F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is pointwise…

Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $\mathbb{G}$ and 1-injectivity of…