Related papers: On Relative Property (T) and Haagerup's Property

We make a comprehensive and self-contained study of compact bicrossed products arising from matched pairs of discrete groups and compact groups. We exhibit an automatic regularity property of such a matched pair and and produce an easy…

In this paper, we discuss some equivalent definitions of Property $\Gamma$ for a type II$_1$ von Neumann algebra. Using these equivalent definitions, we prove that the Pisier's similarity degree of a type II$_1$ von Neumann algebra with…

This paper discusses `geometric property (T)'. This is a property of metric spaces introduced in earlier work of the authors for its applications to K-theory. Geometric property (T) is a strong form of `expansion property': in particular…

Let $\Gamma$ be a discrete countable group. The first main result of this work is that if $\Gamma$ is ICC inner-amenable non-amenable then it cannot satisfy the (AO)-property, answering a question posed by C. Anantharaman-Delaroche. It is…

We prove that relatively hyperbolic groups do not have Lafforgue strong Property $(T)$ with respect to Hilbert spaces. To do so we construct an unbounded affine representation of such groups, whose linear part is of polynomial growth of…

The weak Haagerup property for locally compact groups and the weak Haagerup constant was recently introduced by the second author. The weak Haagerup property is weaker than both weak amenability introduced by Cowling and the first author…

We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra $Q$ of a free group factor $L\Bbb F_n, 2\leq n\leq \infty$ has relative commutant diffuse (i.e. without atoms), then $Q$ is amenable.

We develop a new method, based on non-vanishing of second cohomology groups, for proving the failure of lifting properties for full C$^*$-algebras of countable groups with (relative) property (T). We derive that the full C$^*$-algebras of…

We study abstract finite groups with the property, called property $\hat{s}$, that all of their subrepresentations have submultiplicative spectra. Such groups are necessarily nilpotent and we focus on $p$-groups. $p$-groups with property…

Let $G$ be a connected semisimple Lie group with finite center. Let $\Gamma \subset G$ be a discrete subgroup. We study closed admissible irreducible subrepresentations of the space of distributions $\mathcal S(\Gamma \backslash G)'$…

It is known that for $\sigma$-compact groups Kazhdan's Property $(T)$ is equivalent to Serre's Property $(FH)$. Generalized versions of those properties, called properties $(T_{B})$ and $(F_{B})$, can be defined in terms of the isometric…

We investigate the structure of an alternative finite dimensional $\Q$-algebra $\mathfrak{A}$ subject to the condition that for a $\Z$-order $\Gamma \subset \mathfrak{A}$, and thus for every $\Z$-order of $\mathfrak{A}$, the loop of units…

In this paper we prove that whenever $G$ is hyperbolic relative to a family of exact, ressidually finite subgroups $\{H_1, \ldots, H_n\}$, the corresponding von Neumann algebra $\mathcal L(G)$ is solid relative to the family of subalgebras…

We classify all $G$-invariant von Neumann subalgebras in $L(G)$ for $G=\mathbb{Z}^2\rtimes SL_2(\mathbb{Z})$. This is the first result on classifying $G$-invariant von Neumann subalgebras in $L(G)$ for i.c.c. groups $G$ without the…

Let $G$ and $H$ be locally compact, second countable groups. Assume that $G$ acts in a measure class preserving way on a standard probability space $(X,\mu)$ such that $L^\infty(X,\mu)$ has an invariant mean and that there is a Borel…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i),…

In this paper we study various von Neumann algebraic rigidity aspects for the property (T) groups that arise via the Rips construction developed by Belegradek and Osin in geometric group theory \cite{BO06}. Specifically, developing a new…

We perform a systematic investigation of Kazhdan's relative Property (T) for pairs (G,X), where G a locally compact group and X is any subset. When G is a connected Lie group or a p-adic algebraic group, we provide an explicit…

We consider symmetric random walks on discrete, Zariski-dense subgroups $\Gamma$ of a semisimple Lie group $G$ with Property (T). We prove that if $\Gamma$ has infinite covolume, then the associated hitting measure on the Furstenberg…

Using Godement mean on the Fourier-Stieltjes algebra of a locally compact quantum group we obtain strong separation results for quantum positive-definite functions associated to a subclass of representations, strengthening for example the…