Related papers: Ergodic automorphisms on Kirchberg algebras

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…

We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-space-valued additive…

We give a construction of a nuclear $C^\ast$-algebra associated with an amalgamated free product of groups, generalizing Spielberg's construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic…

We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree…

The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is…

If $G$ acts on a $C^*$-correspondence ${\mathcal H}$, then by the universal property $G$ acts on the Cuntz-Pimsner algebra ${\mathcal O}_{\mathcal H}$ and we study the crossed product ${\mathcal O}_{\mathcal H}\rtimes G$ and the fixed point…

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…

Using Kirchberg-Phillips' classification of purely infinite C*-algebras by K-theory, we prove that the isomorphism types of crossed product C*-algebras associated to certain hyperbolic 3-manifold groups acting on their Gromov boundary only…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector…

We prove that every ergodic amenable action of an algebraic group over a local field of characteristic zero is induced from an ergodic action of an amenable subgroup.

Let $A$ be a separable unital C*-algebra and let $\pi : A \ra \Lc(\Hf)$ be a faithful representation of $A$ on a separable Hilbert space $\Hf$ such that $\pi(A) \cap \Kc(\Hf) = \{0 \}$. We show that $\Oc_E$, the Cuntz-Pimsner algebra…

We prove a new weak mean ergodic theorem (Theorem A) for 1-cocycles associated to weakly mixing representations of amenable groups. Let $G$ be a finitely generated, discrete, amenable group $G$ which admits a controlled Folner sequence. We…

We establish that particular quotients of the non-commutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group $\operatorname*{SU}(n,1)$ of automorphisms of the unit ball in $\mathbb{C}% ^{n}$. To do so, we…

Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their…

For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up to isomorphism. It is trivial if and only…

We consider a construction of C*-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and…

Building on Enders--Schemeitat--Tikuisis' classification, we show that a separable $C^*$-algebra $A$ with approximately inner flip in the UCT class is $K$-theoretically self-absorbing if and only if for every finite group $G$, the Bernoulli…

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes…

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted C*-algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that…