Related papers: Amenability and geometry of semigroups

We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

Let C be a class of groups. We give sufficient conditions ensuring that a free product of residually C groups is again residually C, and analogous conditions are given for locally embeddable into C groups. As a corollary, we obtain that the…

As is well known, the equivalence between amenability of a locally compact group $G$ and injectivity of its von Neumann algebra $\mathcal{L}(G)$ does not hold in general beyond inner amenable groups. In this paper, we show that the…

We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…

We give for a compact group G, a full characterisation of when its Fourier algebra A(G) is weakly amenable: when the connected component of the identity G_e is abelian. This condition is also equivalent to the hyper-Tauberian property for…

We study in this paper the validity of the mean ergodic theorem along \emph{left} F\o lner sequences in a countable amenable group $G$. Although the \emph{weak} ergodic theorem always holds along \emph{any} left F\o lner sequence in $G$, we…

We study the two canonical $\ell^{2}$-Dirichlet structures on a finitely generated group $G$, arising from the left and right regular actions on $\mathbb{R}^{G}$. Although the left and right regular representations are unitarily equivalent,…

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 here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group $G$ on a finite dimensional irreducible CAT(0) cube complex, there is a nonempty $G$-invariant…

Let $f:V\times V\to F$ be a totally arbitrary bilinear form defined on a finite dimensional vector space $V$ over a a field $F$, and let $L(f)$ be the subalgebra of $\gl(V)$ of all skew-adjoint endomorphisms relative to $f$. Provided $F$ is…

Abnormal extremals on four-dimensional connected Lie groups with left-invariant sub-Finsler quasimetric, defined by a seminorm on a two-dimensional subspace of the Lie algebra generating the algebra, are found. In terms of structure…

A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…

We revisit Sz.-Nagy's criteria for similarity of Hilbert space bounded linear operators to isometries or unitaries and present new ones. We also discuss counterparts of the Dixmier-Day theorem concerning bounded representations of amenable…

For a locally compact Abelian group $G$ and a continuous weight function $\omega$ on $G$ we show that the Beurling algebra $L^1(G, \omega)$ is weakly amenable if and only if there is no nontrivial continuous group homomorphism $\phi$: $G\to…

Let $ G $ be a connected Lie group with real Lie algebra $ \mathfrak{g}$. Suppose $G$ is also a complex manifold. We obtain explicit holomorphic sectional and bisectional curvature formulas of left-invariant strongly pseudoconvex complex…

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 provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…