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Abstract
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 we construct a directed graph E such that 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.
Received: 2008-09-01
Revised: 2008-12-08
Published Online: 2010-01-20
Published in Print: 2010-March
© Walter de Gruyter Berlin · New York 2010