Related papers: Classifying crossed product C*-algebras

In this paper we consider the question of what abelian groups can arise as the $K$-theory of $\mathrm{C}^*$-algebras arising from minimal dynamical systems. We completely characterize the $K$-theory of the crossed product of a space $X$…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

Let d be a positive integer, let X be the Cantor set, and let Z^d act freely and minimally on X. We prove that the crossed product C* (Z^d, X) has stable rank one, real rank zero, and cancellation of projections, and that the order on K_0…

Let X be an infinite compact metric space with finite covering dimension and let h be a minimal homeomorphism of X. Let A be the associated crossed product C*-algebra. We show that A has tracial rank zero whenever the image of K_0 (A) in…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

Let $\alpha: G\curvearrowright X$ be a minimal free continuous action of an infinite countable amenable group on an infinite compact metrizable space. In this paper, under the hypothesis that the invariant ergodic probability Borel measure…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…

This paper studies the relationship between minimal dynamical systems on the product of the Cantor set ($X$) and torus ($\T^2$) and their corresponding crossed product $C^*$-algebras. For the case when the cocycles are rotations, we studied…

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

We establish comparison and divisibility properties for crossed product C*-algebras arising from automorphisms of algebras C (X, D) which lie over minimal homeomorphisms, from actions of compact groups which have finite Rokhlin dimension…

We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…

We study the C*-algebra crossed-product of the closed unit disk by the action of one of its conformal automorphisms. After classifying the conformal automorphisms up to topological conjugacy, we investigate, for each class, the irreducible…

We study the matricial field (MF) property for certain reduced crossed product C*-algebras and their traces. Using classification techniques and induced K-theoretic dynamics, we show that reduced crossed products of ASH-algebras of real…

Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction…

We present a systematic study of the structure of crossed products and fixed point algebras by compact group actions with the Rokhlin property on not necessarily unital C*-algebras. Our main technical result is the existence of an…

Let X be an infinite, compact, metrizable space of finite covering dimension and h a minimal homeomorphism of X. We prove that the crossed product of C(X) by h absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a…

The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products.…