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

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dc.creatorMarrero, Alberto
dc.creatorMuhly, Paul S.
dc.date2007-09-14
dc.date.accessioned2026-07-07T08:29:40Z
dc.date.available2026-07-07T08:29:40Z
dc.descriptionInspired 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 $C^*$-algebra of $\mathfrak{G}_{\mathcal{G}}$ is canonically isomorphic to Tomforde's $C^*$-algebra $C^*(\mathcal{G})$. The groupoid $\mathfrak{G}_{\mathcal{G}}$ is built from an inverse semigroup $S_{\mathcal{G}}$ naturally associated to $\mathcal{G}$.
dc.identifierhttps://arxiv.org/abs/0709.2281
dc.identifierhttp://arxiv.org/abs/0709.2281
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138016
dc.subjectOperator Algebras
dc.subjectDynamical Systems
dc.subject46L89
dc.titleGroupoid and Inverse Semigroup Presentations of Ultragraph $C^{*}$-Algebras
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