Related papers: The Path Space of a Directed Graph

We define, for any graph $G=(V,E)$, a boundary $\partial G \subseteq V$. The definition coincides with what one would expected for the discretization of (sufficiently nice) Euclidean domains and contains all vertices from the…

Let $X$ be a topological space. A subset of $C(X)$, the space of continuous real-valued functions on $X$, is a partially ordered set in the pointwise order. Suppose that $X$ and $Y$ are topological spaces, and $A(X)$ and $A(Y)$ are subsets…

The signature of a path, introduced by K.T. Chen [5] in $1954$, has been extensively studied in recent years. The $2010$ paper [12] of Hambly and Lyons showed that the signature is injective on the space of continuous finite-variation paths…

For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a…

There has recently been much interest in the $C^*$-algebras of directed graphs. Here we consider product systems $E$ of directed graphs over semigroups and associated $C^*$-algebras $C^*(E)$ and $\mathcal{T}C^*(E)$ which generalise the…

Finiteness conditions for $C^*$-algebras like AF-embeddability, quasidiagonality, stable finiteness have been studied by many authors and shown to be equivalent for certain classes of $C^*$-algebras. For example, Schfhauser proves that…

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

Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components with $g \geq 2$, $n \geq 0$. Let $\mathcal{N}(R)$ be the nonseparating curve graph, $\mathcal{C}(R)$ be the curve graph and $\mathcal{HT}(R)$ be…

The note is concerned with inductive systems of Toeplitz algebras and their $*$-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup $C^*$-algebra for the additive semigroup of non-negative…

The relative graph $C^*$-algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph $E$ and a subset $R$ of the set of regular vertices of $E$ we show that the…

Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet $X$ and output alphabet $Y$ can be naturally endowed with the quotient of the Euclidean topology by the…

Let D be a domain in C^n with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of…

We consider a locally compact Hausdorff groupoid $G$ which is graded over a discrete group. Then the fibre over the identity is an open and closed subgroupoid $G_e$. We show that both the full and reduced C*-algebras of this subgroupoid…

The core of this note is the observation that links between circle packings of graphs and potential theory developed in \cite{BeSc01} and \cite{HS} can be extended to higher dimensions. In particular, it is shown that every limit of finite…

We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However,…

We define a notion of quantum automorphism group of Graph C*-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of underlying…

Let $G$ be a complex connected reductive algebraic group that acts on a smooth complex algebraic variety $X$, and let $E$ be a $G$-equivariant algebraic vector bundle over $X$. A section of $E$ is regular if it is transversal to the zero…

A Leavitt labelled path algebra over a commutative unital ring is associated with a labelled space, generalizing Leavitt path algebras associated with graphs and ultragraphs as well as torsion-free commutative algebras generated by…

In this article, we identify a suitable approach to define the character space of a commutative unital locally $C^{\ast}$-algebra via the notion of the inductive limit of topological spaces. Also, we discuss topological properties of the…

We show that each pseudoconvex domain $\Omega\subset {\mathbb C}^n$ admits a holomorphic map $F$ to ${\mathbb C}^m$ with $|F|\le C_1 e^{C_2 \hat{\delta}^{-6}}$, where $\hat{\delta}$ is the minimum of the boundary distance and…