Related papers: KMS states on finite-graph C*-algebras
Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS equilibrium states of the resulting C*-dynamical system. We…
We appeal to results from combinatorial random matrix theory to deduce that various random graph $\mathrm{C}^*$-algebras are asymptotically almost surely Kirchberg algebras with trivial $K_1$. This in particular implies that, with high…
Recently, examples of an index theory for KMS states of circle actions were discovered, \cite{CPR2,CRT}. We show that these examples are not isolated. Rather there is a general framework in which we use KMS states for circle actions on a…
Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…
It is shown that the modulus of any graded or, more generally, twisted KMS functional of a C*-dynamical system is proportional to an ordinary KMS state and the twist is weakly inner in the corresponding GNS-representation. If the functional…
We describe a method for associating a $C^{*}$-correspondence to a Mauldin-Williams graph and show that the Cuntz-Pimsner algebra of this $C^{*}$-correspondence is isomorphic to the $C^{*}$-algebra of the underlying graph. In addition, we…
Cuntz algebras $\mathcal{O}_n$, $n>1$, are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding of $\mathcal O_m$ in $\mathcal O_n$ whenever $n-1$ divides…
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…
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 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 apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph $C^*$-algebras. First we give a new proof of non-inner conjugacy of the diagonal MASA ${\mathcal D}_n$ to its…
We determine the factor types of the extremal KMS weights for generalized gauge actions on a graph algebra, and the ground states for the restriction of the action to a corner defined from a vertex. The assumptions on the graph and the…
Given a $k$-graph $\Lambda$ and an element $p$ of $\NN^k$, we define the dual $k$-graph, $p\Lambda$. We show that when $\Lambda$ is row-finite and has no sources, the $C^*$-algebras $C^*(\Lambda)$ and $C^*(p\Lambda)$ coincide. We use this…
We present a detailed exposition (for a Dynamical System audience) of the content of the paper: R. Exel and A. Lopes, $C^*$ Algebras, approximately proper equivalence relations and Thermodynamic Formalism, {\it Erg. Theo. and Dyn. Syst.},…
In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an…
We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph…
In the framework of deformation quantization we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[\lambda]]-linear functionals obeying a formal variant of the usual KMS…
In this paper we give a complete description of K-theory groups for Cuntz-Krieger C*-algebras associated to general locally-finite (topologically connected) graphs via Bass-Hashimoto operator. Our result generalizes the one obtained by the…
To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…
We describe KMS-states on the C*-algebras of etale groupoids in terms of measurable fields of traces on the C*-algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid C*-algebras and…