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

10 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

Fingerprint

Graph Algebra
Morita Equivalence
Algebra
Real Rank Zero
Directed Graph
Gauge
Quotient
Directed graphs
Isomorphic
Gages
Invariant

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence. / Katsura, Takeshi; Muhly, Paul S.; Sims, Aidan; Tomforde, Mark.

In: Journal fur die Reine und Angewandte Mathematik, No. 640, 03.2010, p. 135-165.

Research output: Contribution to journalArticle

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