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

Takeshi Katsura, Paul S. Muhly, Aidan Sims, Mark Tomforde

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)135-165
Number of pages31
JournalJournal fur die Reine und Angewandte Mathematik
Issue number640
DOIs
Publication statusPublished - 2010 Mar 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence'. Together they form a unique fingerprint.

  • Cite this