Abstract
Inspired by the work of Paterson on C *-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 \(\mathcal{G}\) .
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Communicated by László Márki
A.E. Marrero was supported by grants from the National Science Foundation and the Sloan Foundation and by a GAANN Fellowship. Many of the results here are taken from this author’s dissertation [7].
P.S. Muhly was supported by a grant from the National Science Foundation (DMS-0355443).
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Marrero, A.E., Muhly, P.S. Groupoid and inverse semigroup presentations of ultragraph C *-algebras. Semigroup Forum 77, 399–422 (2008). https://doi.org/10.1007/s00233-008-9046-8
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DOI: https://doi.org/10.1007/s00233-008-9046-8