Related papers: Maximal amenable subgroups of arithmetic groups

We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of…

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups.…

We prove several theorems relating amenability of groups in various categories (discrete, definable, topological, automorphism group) to model-theoretic invariants (quotients by connected components, Lascar Galois group, G-compactness,…

The groups distinguish their von Neumann algebras, in the case when these are factors.

We describe finite soluble groups in which every $n$-maximal subgroup is $\mathfrak F$-subnormal.

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…

We show that free Burnside groups of sufficiently large odd exponent are non--amenable in a certain strong sense, more precisely, their left regular representations are isolated from the trivial representation uniformly on finite generating…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then…

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse…

We continue our study of the concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele and our investigation of their relationship with nuclearity and injectivity. One major tool for our analysis…

The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic $p>3$. All maximal…

We develop the theory of algorithmic randomness for the space $A^G$ where $A$ is a finite alphabet and $G$ is a computable amenable group. We give an effective version of the Shannon-McMillan-Breiman theorem in this setting. We also extend…

Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…

Let $T$ be a Banach algebra homomorphism from a Banach algebra $\mathcal B$ to a Banach algebra $\mathcal A$ with $\|T\|\leq 1$. Recently it has been obtained some results about Arens regularity and also various notions of amenability of…

We consider a paving property for a maximal abelian *-subalgebra (MASA) $A$ in a von Neumann algebra $M$, that we call so-paving, involving approximation in the so-topology, rather than in norm (as in classical Kadison-Singer paving). If…

In this paper, we introduce the new notion of strong pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion to the various notions of Connes amenability. Also we show that for every non-empty set…

We study the range of a classifiable class ${\cal A}$ of unital separable simple amenable $C^*$-algebras which satisfy the Universal Coefficient Theorem. The class ${\cal A}$ contains all unital simple AH-algebras. We show that all unital…

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.

We prove a quantized version of a theorem by M. V. Sheinberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

We study maximal horizontal subgroups of Carnot groups of Heisenberg type. We classify those of dimension half of that of the canonical distribution ("lagrangians") and illustrate some notable ones of small dimension. An infinitesimal…