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

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Katsura, Takeshi
Muhly, Paul S.
Sims, Aidan
Tomforde, Mark
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We 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.
Comment: 29 pages, 1 figure; Version 2 Comments: Minor changes and a few small typos corrected
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Mathematics - Operator Algebras, 46L55
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