Related papers: Separating a chart

Let $\Gamma$ be a chart, and we denote by $\Gamma_m$ the union of all the edges of label $m$. A chart $\Gamma$ is of type $(3,2,2)$ if there exists a label $m$ such that $w(\Gamma)=7$, $w(\Gamma_m\cap\Gamma_{m+1})=3$,…

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

The divisibility graph $D(G)$ for a finite group $G$ is a graph with vertex set $cs~(G)\setminus\{1\}$ where $cs~(G)$ is the set of conjugacy class sizes of $G$. Two vertices $a$ and $b$ are adjacent whenever $a$ divides $b$ or $b$ divides…

For Denjoy--Carleman differential function classes $C^M$ where the weight sequence $M=(M_k)$ is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is $C^M$ if it…

A {\it graph product} $G$ on a graph $\Gamma$ is a group defined as follows: For each vertex $v$ of $\Gamma$ there is a corresponding non-trivial group $G_v$. The group $G$ is the quotient of the free product of the $G_v$ by the commutation…

We show that if $(A,G,\alpha)$ is a groupoid dynamical system with $A$ continuous trace, then the crossed product $A\rtimes_{\alpha}G$ is Morita equivalent to the C*-algebra $C*(\underline G,\underline E)$ of a twist $\underline E$ over a…

We prove that the C*-algebra of the universal (n,m)-dynamical system may be obtained, up to Morita-Rieffel equivalence, as the crossed-product relative to an interaction on a commutative C*-algebra. The interaction involved is shown not to…

In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.

The necessary and suffcient condition for a set of matrices to commute is given and proven.

Suppose that $\Gamma$ is a non-empty connected graph, $\mathfrak{G}$ is the fundamental group of a graph of groups over $\Gamma$, and $\mathcal{C}$ is a root class of groups (the last means that $\mathcal{C}$ contains non-trivial groups and…

Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism $\pi$ from C to M. Let u: A --> M be a decomposable map (i.e. a linear combination of completely positive maps) which is a…

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of…

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…

Let $G$ a bipartite graph with vertex bipartition $\{A,B\}$ and let $m=|E(G)|$. An $(A,B)$-uniformly ordered labeling of $G$ is a labeling $f\colon V\rightarrow [0,2m]$ which, among other conditions, requires that there exists $\lambda\in…

Let $\Gamma$ be a countable group and $(X, \Gamma)$ a compact topological dynamical system. We study the question of the existence of an intermediate $C^*$-subalgebra $\mathcal{A}$ $$C^{*}_{r}(\Gamma)<\mathcal{A}<C(X)\rtimes_r\Gamma,$$…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…

Let $A$, $B$ be separable C*-algebras, $B$ stable. Elements of the E-theory group $E(A,B)$ are represented by asymptotic homomorphisms from the second suspension of $A$ to $B$. Our aim is to represent these elements by (families of) maps…

The problem of inner vs outer conjugacy of subalgebras of certain graph C*-algebras is investigated. For a large class of finite graphs E, we show that whenever $\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

We study the Hamiltonian path problem in C-shaped grid graphs, and present the necessary and sufficient conditions for the existence of a Hamiltonian path between two given vertices in these graphs. We also give a linear-time algorithm for…