Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence

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dc.creatorKatsura, Takeshi
dc.creatorMuhly, Paul S.
dc.creatorSims, Aidan
dc.creatorTomforde, Mark
dc.date2008-09-01
dc.date2008-12-09
dc.date.accessioned2026-07-07T12:09:56Z
dc.date.available2026-07-07T12:09:56Z
dc.descriptionWe prove that the classes of graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. This result answers the long-standing open question of whether every Exel-Laca algebra is Morita equivalent to a graph algebra. Given an ultragraph G we construct a directed graph E such that C*(G) is isomorphic to a full corner of C*(E). As applications, we characterize real rank zero for ultragraph algebras and describe quotients of ultragraph algebras by gauge-invariant ideals.
dc.description29 pages, 1 figure; Version 2 Comments: Minor changes and a few small typos corrected
dc.identifierhttps://arxiv.org/abs/0809.0164
dc.identifierhttp://arxiv.org/abs/0809.0164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209797
dc.subjectOperator Algebras
dc.subject46L55
dc.titleGraph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
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