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

A coaction d of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A times_d G times_{d hat} G onto A otimes K(L^2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are…

Actions of a locally compact group G on a measure space X give rise to unitary representations of G on Hilbert spaces. We review results on the rigidity of these actions from the spectral point of view, that is, results about the existence…

We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.

It is known that if each point $x$ of a dynamical system is generic for some invariant measure $\mu_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group…

In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory and set theory. In addition to a statement and proof of…

Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was…

We investigate the representation theory of the crossed-product C*-algebra associated to a compact group G acting on a locally compact space X when the stability subgroups vary discontinuously. Our main result applies when G has a principal…

We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable,…

Let $ G $ be a countable discrete group and consider a nonsingular Bernoulli shift action $ G \curvearrowright \prod_{g\in G }(\{0,1\},\mu_g)$ with two base points. When $ G $ is exact, under a certain finiteness assumption on the measures…

We consider a crossed product of a unital simple separable nuclear stably finite Z-stable C*-algebra A by a strongly outer cocycle action of a discrete countable amenable group \Gamma. Under the assumption that A has finitely many extremal…

We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…

A discrete group $\G$ is called rigidly symmetric if for every $C^*$-algebra $\A$ the projective tensor product $\ell^1(\G)\widehat\otimes\A$ is a symmetric Banach $^*$-algebra. For such a group we show that the twisted crossed product…

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules as the ones of SO(3). As consequences, we get (1) a…

In the setting of product systems over group-embeddable monoids, we consider nuclearity of the associated Toeplitz C*-algebra in relation to nuclearity of the coefficient algebra. Our work goes beyond the known cases of single…

Given a dynamical system $(X, \Gamma)$, the corresponding crossed product $C^*$-algebra $C(X)\rtimes_{r}\Gamma$ is called reflecting, when every intermediate $C^*$-algebra $C^*_r(\Gamma)<\mathcal{A} < C(X)\rtimes_{r}\Gamma$ is of the form…

Let $X$ be an algebraic variety over $\mathbb{C}$ and $G$ be an algebraic group acting on $X$ whose action is closed. J. Poineau defined a compactification $X^\urcorner$ of $X(\mathbb{C})$ by using hybrid Berkovich spaces. We will focus on…

The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the…

We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…

An \textit{algebraic} action of a discrete group $\Gamma $ is a homomorphism from $\Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $\Gamma $ is determined by a module…