Related papers: Weighted Cuntz-Krieger Algebras

We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

We show that every strongly $\mathbb{Z}$-graded C*-algebra (equivalently, every C*-algebra carrying a strongly continuous $\mathbb{T}$-action with full spectral subspaces) is a Cuntz--Pimsner algebra, and describe subalgebras and subspaces…

To a directed graph $E$ is associated a $C^*$-algebra $C^* (E)$ called a graph $C^*$-algebra. There is a canonical action $\gamma$ of ${\bf T}$ on $C^* (E)$, called the gauge action. In this paper we present necessary and sufficient…

Let $F$ be the Fibonacci matrix $ \bigl[\begin{smallmatrix} 1 & 1 1 & 0 \\ \end{smallmatrix}\bigr] $. The Fibonacci Dyck shift is a subshsystem of the Dyck shift $D_2$ constrained by the matrix $F$. Let ${{\frak L}^{Ch(D_F)}}$ be a…

We consider Exel's interaction $(V,H)$ over a unital $C^*$-algebra $A$, such that $V(A)$ and $H(A)$ are hereditary subalgebras of $A$. For the associated crossed product, we obtain a uniqueness theorem, ideal lattice description, simplicity…

The (abstract) Cuntz algebra is generated by non-unitary isometries and has therefore no intrinsic finiteness properties. To approximate the elements of the Cuntz algebra by finite-dimensional objects, we thus consider a spatial…

Given a locally compact group $G$ and a unitary representation $\rho:G\to U({\mathcal H})$ on a Hilbert space ${\mathcal H}$, we construct a $C^*$-correspondence ${\mathcal E}(\rho)={\mathcal H}\otimes_{\mathbb C} C^*(G)$ over $C^*(G)$ and…

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…

We present and study C*-algebras generated by "periodic weighted creation operators" on the Fock space associated with an automorphism $\alpha$ on a C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens algebras…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

In this paper, we consider pure infiniteness of generalized Cuntz-Krieger algebras associated to labeled spaces $(E,\mathcal{L},\mathcal{E})$. It is shown that a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{E})$ is purely infinite in the sense…

Let ${\cal O}_{{\cal H}^{A,B}_\kappa}$ be the $C^*$-algebra associated with the Hilbert $C^*$-quad module arising from commuting matrices $A,B$ with entries in $\{0,1\}$. We will show that if the associated tiling space $X_{A,B}^\kappa$ is…

In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge…

Cuntz algebra $\mathcal O_2$ is the universal $C^*$-algebra generated by two isometries $s_1, s_2$ satisfying $s_1s_1^*+s_2s_2^*=1$. This is separable, simple, infinite $C^*$-algebra containing a copy of any nuclear $C^*$-algebra. The…

For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra…

Let $\mathcal{G}$ be a quantum graph without quantum sources and $E_\mathcal{G}$ be the quantum edge correspondence for $\mathcal{G}.$ Our main results include sufficient conditions for simplicity of the Cuntz-Pimsner algebra…

For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C*(E).

We present a class of subshifts $Z_N, N = 1,2,...$ whose associated $C^*$-algebras ${\cal O}_{Z_N}$ are simple, purely infinite and not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The class of the subshifts is the…

Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*_{min}(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections…