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Graph algebras, exel-laca algebras, and ultragraph algebras coincide up to Morita equivalence

Journal Article


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 $\G$ we construct a directed graph $E$ such that $C^*(\G)$ 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.

UOW Authors


  •   Katsura, Takeshi (external author)
  •   Muhly, Paul S. (external author)
  •   Sims, Aidan
  •   Tomforde, Mark (external author)

Publication Date


  • 2010

Citation


  • Katsura, T., Muhly, P. S., Sims, A. & Tomforde, M. (2010). Graph algebras, exel-laca algebras, and ultragraph algebras coincide up to Morita equivalence. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, (640), 135-165.

Scopus Eid


  • 2-s2.0-77951537410

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3416

Number Of Pages


  • 30

Start Page


  • 135

End Page


  • 165

Issue


  • 640

Place Of Publication


  • http://www.reference-global.com/loi/crll

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 $\G$ we construct a directed graph $E$ such that $C^*(\G)$ 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.

UOW Authors


  •   Katsura, Takeshi (external author)
  •   Muhly, Paul S. (external author)
  •   Sims, Aidan
  •   Tomforde, Mark (external author)

Publication Date


  • 2010

Citation


  • Katsura, T., Muhly, P. S., Sims, A. & Tomforde, M. (2010). Graph algebras, exel-laca algebras, and ultragraph algebras coincide up to Morita equivalence. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, (640), 135-165.

Scopus Eid


  • 2-s2.0-77951537410

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3416

Number Of Pages


  • 30

Start Page


  • 135

End Page


  • 165

Issue


  • 640

Place Of Publication


  • http://www.reference-global.com/loi/crll