Related papers: Separating a chart

We characterize the lifting property (LP) of a separable $C^*$-algebra $A$ by a property of its maximal tensor product with other $C^*$-algebras, namely we prove that $A$ has the LP if and only if for any family $(\{D_i\mid i\in I\}$ of…

This paper contains a quite detailed description of the C*-algebra arising from the transformation groupoid of a rational map of degree at least two on the Riemann sphere. The algebra is decomposed stepwise via extensions of familiar…

This partly expository paper first supplies the details of a method of factoring a stable C*-algebra A as B \otimes K in a canonical way. Then it is shown that this method can be put into a categorical framework, much like the…

A matching $M$ in a graph $\Gamma$ is positive if $\Gamma$ has a vertex-labeling such that $M$ coincides with the set of edges with positive weights. A positive matching decomposition (pmd) of $\Gamma$ is an edge-partition $M_1,\ldots,M_p$…

In this this paper we introduce entanglement among the points in a non-commutative scheme, in addition to the tangent directions. A diagram of $A$-modules is a pair $\uc=(|\uc|,\Gamma)$ where $|\uc|={V_1,...,V_r}$ is a set of $A$-modules,…

Let $f:\mathbb{D}\to\mathbb{C}$ be a bounded analytic function. A set $K\subset\mathbb{D}$ which contains the point $1$ in its boundary is called a convergence set for $f$ at $1$ if $f(z)$ converges to some value $\zeta$ as $z\to1$ with…

We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…

In this paper, two outwardly different graphs, namely, the zero divisor graph $\Gamma(C_c(X))$ and the comaximal graph $\Gamma_2^{'}(C_c(X))$ of the ring $C_c(X)$ of all real-valued continuous functions having countable range, defined on…

Given a countable abelian group $A$, we construct a row finite directed graph $\Gamma(A)$ such that the $K_{0}$-group of the graph $\textrm{C}^{\ast}$-algebra $\textrm{C}^{\ast}(\Gamma(A))$ is canonically isomorphic to $A$. Moreover, each…

We prove that if d is an integer number bigger than 1 and f_1,...,f_d are commuting circle diffeomorphisms respectively of class C^(1+\tau_k), where \tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate to rotations…

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all…

We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first equivalent formulation of shift equivalence of essential…

Let $G$ be a finite, non-abelian group of the form $G = A N$, where $A \leq G$ is abelian, and $N \trianglelefteq G$ is cyclic. We prove that the commuting graph $\Gamma(G)$ of $G$ is either a connected graph of diameter at most four, or…

Let $\Gamma$ be a simple connect graph on a finite vertex set $V$ and let $A$ be its adjacency matrix. Then $\Gamma$ is said to be \textit{singular} if and only if $0$ is an eigenvalue of $A.$ The \textit{nullity (singularity)} of $\Gamma,$…

We consider two types of geometric graphs on point sets on the plane based on a plane set C: one obtained by translates of C, another by positively scaled translates (homothets) of C. For compact and convex C, graphs defined by scaled…

A {\it separated graph} is a pair $(E,C)$ consisting of a directed graph $E$ and a set $C=\bigsqcup_{v\in E^0}C_v$, where each $C_v$ is a partition of the set of edges whose terminal vertex is $v$. Given a separated graph $(E,C)$, such that…

We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…

A $\lambda$-graph system $\frak L$ is a labeled Bratteli diagram with shift operation. It is a generalized notion of finite labeled graph and presents a subshifts. We will study continuous orbit equivalence of one-sided subshifts and…

We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.

We consider separable $C^*$-dynamical systems $(A,G,\alpha)$ for which the induced action of the group $G$ on the spectrum $\hat A$ of the $C^*$-algebra $A$ is free. We study how the representation theory of the associated crossed-product…