Related papers: A class of groups for which every action is W*-sup…

It is shown that, for an arbitrary free and minimal $\mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $\mathrm{C}(X)\rtimes\mathbb Z^n$ always has stable rank one, i.e., invertible elements are dense.…

In this short note we classify the Cartan subalgebras in all von Neumann algebras associated with graph product groups and their free ergodic measure preserving actions on probability spaces.

We prove several superrigidity results for isometric actions on metric spaces satisfying some convexity properties. First, we extend some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of…

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

Let \alpha_0 be an affine action of a discrete group \Gamma on a compact homogeneous space X and \alpha_1 a smooth action of \Gamma on X which is C^1-close to \alpha_0. We show that under some conditions, every topological conjugacy between…

Let G=PSL(2, F) where F= R or C, and consider the space Z=(\Gamma_1 x \Gamma_2)\ (G x G) where \Gamma_1<G is a co-compact lattice and \Gamma_2<G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint gives a…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

Let $\Gamma$ be a nonelementary discrete subgroup of SU(n,1) or Sp(n,1). We show that if the trace field of $\Gamma$ is contained in $\mathbb R$, $\Gamma$ preserves a totally geodesic submanifold of constant negative sectional curvature.…

We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…

We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra L(G) completely "remembers" the group G. More precisely, if L(G) is isomorphic to the von Neumann algebra…

A discrete group $G$ is called W*-superrigid if the group $G$ can be entirely recovered from the ambient group von Neumann algebra $L(G)$. We introduce an analogous notion for discrete quantum groups. We prove that this strengthened quantum…

In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $\Gamma$. Let $\alpha\colon G\to \mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property.…

Let $G$ be a connected semisimple real algebraic group and $\Gamma<G$ be its Zariski dense discrete subgroup. We prove that if $\Gamma\backslash G$ admits any finite Bowen-Margulis-Sullivan measure, then $\Gamma$ is virtually a product of…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma<G$ a discrete subgroup. For a large class of…

In this paper, we deal with the $\mathcal{U}(\mathfrak{g})$-action on a $\mathfrak{g}$-module on which a larger algebra $\mathcal{A}$ acts irreducibly. Under a mild condition, we will show that the support of the…

We show that an ergodic measure preserving action $\Gamma \curvearrowright (X,\mu)$ of a discrete group $\Gamma$ on a $\sigma$-finite measure space $(X,\mu)$ satisfies the local spectral gap property (introduced by Boutonnet, Ioana and…

We prove that if $G$ is a countable discrete group with property (T) over an infinite subgroup $H<G$ which contains an infinite Abelian subgroup or is normal, then $G$ has continuum many orbit inequivalent measure preserving a.e. free…

We prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, in certain higher-rank groups into unitary groups of finite factors. This extends the authors' previous work…