Groupoid and Inverse Semigroup Presentations of Ultragraph $C^{\ast }$-Algebras

Abstract

Inspired by the work of Paterson on $C^{\ast }$-algebras of directed graphs, we show how to associate a groupoid ${\mathfrak{G}}_{\mathcal{G}}$ to an ultragraph $\mathcal{G}$ in such a way that the $C^{\ast }$-algebra of ${\mathfrak{G}}_{\mathcal{G}}$ is canonically isomorphic to Tomforde's $C^{\ast }$-algebra $C^{\ast }(\mathcal{G})$. The groupoid ${\mathfrak{G}}_{\mathcal{G}}$ is built from an inverse semigroup $S_{\mathcal{G}}$ naturally associated to $\mathcal{G}$.

References in corpus (1)

• Ultragraph C*-algebras via topological quivers