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

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

研究成果: Article査読

14 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)135-165
ページ数31
ジャーナルJournal fur die Reine und Angewandte Mathematik
640
DOI
出版ステータスPublished - 2010 3

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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