Related papers: Rigidity theory for $C^*$-dynamical systems and th…

A group of bijections G acting on a set X is said with fixed points (abbreviated as gaf from the french "groupe {\`a} points fixes") if any element of G has at least one fixed point in X. The G group is said with a common fixed point…

We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…

Suppose a locally compact group G acts freely and properly on a locally compact Hausdorff space X, and let gamma be the induced action on C_0(X). We consider a category in which the objects are C*-dynamical systems (A, G, alpha) for which…

We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_{\Gamma}$. We show that, under certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an…

For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, the logarithmic capacity $c_{\beta}$, and the analytic capacity $c_{B}$ satisfy the inequality chain $\pi K \geq c^2_{\beta} \geq c^2_B$; moreover, equality holds at a…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $\Gamma$ acting on a compact space $X$ and a subgroup $H$, we…

Given a discrete group $G$, we identify the Stone-$\check C$ech compactification $\beta G$ with the set of all ultrafilters on $G$ and put $G^\ast =\beta G\setminus G$. The action $G$ on $G$ by the conjugations $(g,x)\mapsto g^{-1}xg$…

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…

Three properness conditions for actions of locally compact groups on C*-algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are…

Given a C*-algebra $A$, a discrete abelian group $X$ and a homomorphism $\Theta: X\to$ Out$A$ defining the dual action group $\Gamma\subset$ aut$A$, the paper contains results on existence and characterization of Hilbert $\{A,\Gamma\}$,…

We consider a fixed free and proper action of a locally compact group $G$ on a space $T$, and actions $\alpha:G\to \Aut A$ on $C^*$-algebras for which there is an equivariant embedding of $(C_0(T),\rt)$ in $(M(A),\alpha)$. A recent theorem…

We generalize W*-superrigidity results about Bernoulli actions of rigid groups to general mixing Gaussian actions. We thus obtain the following: If \Gamma\ is any ICC group which is w-rigid (i.e. it contains an infinite normal subgroup with…

In this paper we study rigidity properties of abelian \hyphenation{break-able}actions with weak or no hyperbolicty. We introduce a general strategy for proving $C^\infty$ local rigidity of algebraic actions. As a consequence, we show…

Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global…

We show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…

Given a discrete group $\Gamma$, a finite factor $\mathcal N$ and a real number $p\in [1, +\infty)$ with $p\neq 2,$ we are concerned with the rigidity of actions of $\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\mathcal N)$…

We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove…

We analzye Rieffel's construction of generalized fixed point algebras in the setting of group actions on Hilbert modules. Let G be a locally compact group acting on a C*-algebra B. We construct a Hilbert module F over the reduced crossed…

A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…