TY - JOUR
T1 - Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
AU - Katsura, Takeshi
AU - Muhly, Paul S.
AU - Sims, Aidan
AU - Tomforde, Mark
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010/3
Y1 - 2010/3
N2 - 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 script G sign we construct a directed graph E such that C*(script G sign) 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.
AB - 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 script G sign we construct a directed graph E such that C*(script G sign) 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.
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U2 - 10.1515/CRELLE.2010.023
DO - 10.1515/CRELLE.2010.023
M3 - Article
AN - SCOPUS:77951537410
SN - 0075-4102
SP - 135
EP - 165
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 640
ER -