Related papers: Haagerup approximation property via bimodules

Suppose $\mathcal{A}$ is a separable unital ASH C*-algebra, $\mathcal{R}$ is a sigma-finite II$_{\infty}$ factor von Neumann algebra, and $\pi,\rho :\mathcal{A}\rightarrow\mathcal{R}$ are unital $\ast$-homomorphisms such that, for every…

For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of…

Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the Haagerup property, then the wreath product…

The notions of a box family and fibred cofinitely-coarse embedding are introduced. The countable, residually amenable groups satisfying the Haagerup property are then characterized as those possessing a box family that admits a fibred…

For a locally compact group G, the convolution product on the space N(L^p(G)) of nuclear operators was defined by Neufang. We study homological properties of the convolution algebra N(L^p(G)) and relate them with some properties of the…

Around 1967, Arveson invented a striking noncommutative generalization of classical $H^\infty$, known as {\em subdiagonal algebras}, which include a wide array of examples of interest to operator theorists. Their theory extends that of the…

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…

We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic…

We generalise the definition of a group algebra so that it makes sense for non-locally compact topological groups, in particular, we require that the representation theory of the group algebra is isomorphic (in the sense of Gelfand-Raikov)…

Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain…

Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate…

We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the graphical C'(lambda)-small cancellation condition with respect to graphs endowed with a compatible…

Let K >= 1 be a parameter. A K-approximate group is a finite set A in a (local) group which contains the identity, is symmetric, and such that A^2 is covered by K left translates of A. The main result of this paper is a qualitative…

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is…

We prove that the category of ordered abelian groups equipped with an automorphism has the Amalgamation Property, deduce that their inductive theory is NIP in the sense of positive logic, and initiate a development of the latter framework.…

Our main result is that for densities $<\frac{3}{10}$ a random group in the square model has the Haagerup property and is residually finite. Moreover, we generalize the Isoperimetric Inequality, to some class of non-planar diagrams and,…

We show that Drinfeld's double group construction for locally compact quantum groups preserves the Haagerup property. This shows that the Drinfeld doubles of the quantum groups, $C_{0}(\mathbb{F}_{2})$, $SU_{q}(2)$,…

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a…

Let $\mathcal G$ be the Cayley graph of a finitely generated, infinite group $\Gamma$. We show that $\Gamma$ has the Haagerup property if and only if for every $\alpha<1$, there is a $\Gamma$-invariant bond percolation $\mathbb P$ on…

An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…