Related papers: A class of simple $C^*$-algebras arising from cert…

In this paper we give a formula for the $K$-theory of the $C^*$-algebra of a weakly left-resolving labelled space. This is done by realising the $C^*$-algebra of a weakly left-resolving labelled space as the Cuntz-Pimsner algebra of a…

We define the categorical cohomology of a k-graph \Lambda\ and show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative…

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…

We use product systems of $C^*$-correspondences to introduce twisted $C^*$-algebras of topological higher-rank graphs. We define the notion of a continuous $\mathbb{T}$-valued $2$-cocycle on a topological higher-rank graph, and present…

Let A be a unital simple separable C*-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray-von Neumann semigroup and the tracial state space T(A) whenever the…

The paper contains a description of the KMS weights for the one-parameter action on the reduced C*-algebra of a second countable locally compact Hausdorff etale groupoid, arising from a continuous real valued homomorphism satisfying two…

Let $G$ be a compact quantum group. We show that given a $G$-equivariant $\mathrm{C}^*$-correspondence $E$, the Pimsner algebra $\mathcal{O}_E$ can be naturally made into a $G$-$\mathrm{C}^*$-algebra. We also provide sufficient conditions…

When a locally compact group acts on a C*-correspondence, it also acts on the associated Cuntz-Pimsner algebra in a natural way. Hao and Ng have shown that when the group is amenable the Cuntz-Pimsner algebra of the crossed product…

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…

We study KMS states for gauge actions with potential functions on Cuntz--Krieger algebras whose underlying one-sided topological Markov shifts are continuous orbit equivalent. As a result, we have a certain relationship between topological…

Given a C$^*$-algebra $A$ with an almost periodic time evolution $\sigma$, we define a new C$^*$-algebra $A_c$, which we call the crystal of $(A,\sigma)$, that represents the zero temperature limit of $(A, \sigma)$. We prove that there is a…

We study the equilibrium or KMS states of the Toeplitz C*-algebra of a finite higher-rank graph which is reducible. The Toeplitz algebra carries a gauge action of a higher-dimensional torus, and a dynamics arises by choosing an embedding of…

We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group $\Gamma$ and any infinite group $\Lambda$, we construct an outer action of $\Lambda$ on the Cuntz algebra…

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

For each odd integer $n \geq 3$, we construct a rank-3 graph $\Lambda_n$ with involution $\gamma_n$ whose real C*-algebra $C^*_\mathbb{R}(\Lambda_n, \gamma_n)$ is stably isomorphic to the exotic Cuntz algebra $\mathcal E_n^\mathbb{R}$. This…

We study uniformly recurrent subgroups (URS) introduced by Glasner and Weiss \cite{GW}. Answering their query we show that any URS $Z$ of a finitely generated group is the stability system of a minimal $Z$-proper action. We also show that…

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…

To a graph $\Gamma$ one can associate a C^*-algebra $C^*(\Gamma)$ generated by isometries. Such $C^*$-algebras were studied recently by Crisp and Laca. They are a special case of the Toeplitz C^*-algebras $\mathcal{T}(G, P)$ associated to…

The notion of almost elementariness for a locally compact Hausdorff \'{e}tale groupoid $\mathcal{G}$ with a compact unit space was introduced by the authors as a sufficient condition ensuring the reduced groupoid $C^*$-algebra…

We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph. This is done by a purely graph theoretical calculation of the K-theory and the position of the unit…