Related papers: Strongly self-absorbing C*-dynamical systems, III

In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being self-adjoint, and another being non-self-adjoint.…

We establish four results concerning connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. For actions of residually finite groups or of the reals which have finite…

We classify equivariant *-homomorphisms between C*-dynamical systems associated to actions of finite groups on C*-algebras with the Rokhlin property. In addition, the given actions are classified. An obstruction is obtained for the Cuntz…

We revisit Matui-Sato's notion of property (SI) for C*-algebras and C*-dynamics. More specifically, we generalize the known framework to the case of C*-algebras with possibly unbounded traces. The novelty of this approach lies in the…

Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra…

Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant…

C*-bundle dynamical systems are introduced and their r\^ole within the theory of C*-subalgebras and Fell bundles is investigated. A C*-bundle dynamical system involves an action of a 1-parameter group of "spatial automorphisms" of the…

We prove that unique ergodicity of tensor product of $C^*$-dynamical system implies its strictly weak mixing. By means of this result a uniform weighted ergodic theorem with respect to $S$-Besicovitch sequences for strictly weak mixing…

To a given multivariable C*-dynamical system $(A, \al)$ consisting of *-automorphisms, we associate a family of operator algebras $\alg(A, \al)$, which includes as specific examples the tensor algebra and the semicrossed product. It is…

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^*$-algebras $A$ and $B$ are outer conjugate if and only if there is an isomorphism of the crossed products that is…

We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam. This result has several…

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any…

Fell's absorption principle states that the left regular representation of a group absorbs any unitary representation of the group when tensored with it. In a weakened form, this result carries over to the left regular representation of a…

We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras,…

We show that the Fra\"iss\'e limit of a category of unital separable $C^*$-algebras which is sufficiently closed under tensor products of its objects and morphisms is strongly self-absorbing, given that it has approximate inner half-flip.…

This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…

We calculate the Cuntz semigroup of the tensor product A with A. We restrict our attention to C*-algebras A which are unital, simple, nuclear, stably finite, have stable rank one, absorbs the Jiang-Su algebra tensorially and satisfy the…

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C*-module is isomorphic to a direct summand in the standard module of square summable sequences in the base C*-algebra. In this paper, this…

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank…

We prove that the infinite tensor power of a unital separable C*-algebra absorbs the Jiang-Su algebra Z tensorially if and only if it contains, unitally, a subhomogeneous algebra without characters. This yields a succinct universal property…