Related papers: Partial dynamical systems and AF C*-algebras

We show that if X is a finite dimensional locally compact Hausdorff space, then the crossed product of C_0(X) by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be…

Starting from a Hopf algebra endowed with an action of a group G by Hopf automorphisms, we construct (by a twisted double method) a quasitriangular Hopf G-coalgebra. This method allows us to obtain non-trivial examples of quasitriangular…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

We introduce the fundamental group $\r{F}(\c{A})$ of a unital $C^*$-algebra $\c{A}$ with finite dimensional trace space. The elements of fundamental group are restricted by K-theoretical obstruction and positivity. Moreover we show there…

We give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory,…

We study partial homology and cohomology from ring theoretic point of view via the partial group algebra $\mathbb{K}_{par}G$. In particular, we link the partial homology and cohomology of a group $G$ with coefficients in an irreducible…

To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…

We study Blackadar and Kirchberg's matricial field (MF) property and quasidiagonality in cross-sectional C*-algebras constructed from Fell Bundles and, in particular, from partial C*-dynamical systems. In doing so we generalize Kerr and…

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…

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the constructions of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most…

We study semigroup C*-algebras of $ax+b$-semigroups over integral domains. The goal is to generalize several results about C*-algebras of $ax+b$-semigroups over rings of algebraic integers. We prove results concerning K-theory and…

After investigating by examples the unusual and striking elementary properties of the Penrose tilings and the Arnold cat map, we associate a finite symbolic dynamics with finite grammar rules to each of them. Instead of studying these…

We study the finite versus infinite nature of C*-algebras arising from etale groupoids. For an ample groupoid G, we relate infiniteness of the reduced C*-algebra of G to notions of paradoxicality of a K-theoretic flavor. We construct a…

We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C*-algebras (sometimes also referred to as diagonal C*-pairs). Our concept has good permanence properties and detects more refined information than nuclear…

We compute the K-theory of the three C*-algebras associated to a rational function R acting on the Riemann sphere, its Fatou set, and its Julia set. The latter C*-algebra is a unital UCT Kirchberg algebra and is thus classified by its…

Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…

We compute the $ K $-theory of quantum automorphism groups of finite dimensional $ C^* $-algebras in the sense of Wang. The results show in particular that the $ C^* $-algebras of functions on the quantum permutation groups $ S_n^+ $ are…

It is proved that the K_0-group of a cluster C*-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture for cluster algebras. As an example, we consider a cluster…

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…

The paper contains a description of a connection between diagonal actions and certain KMS weights on groupoid $C^{*}$-algebras. It furthermore contains the realization of a graph $C^{*}$-algebra of a countable graph as the groupoid…