A+ CATEGORY SCIENTIFIC UNIT

Ultragraph $C^*$-algebras via topological quivers

Volume 187 / 2008

Takeshi Katsura, Paul S. Muhly, Aidan Sims, Mark Tomforde Studia Mathematica 187 (2008), 137-155 MSC: Primary 46L05. DOI: 10.4064/sm187-2-3

Abstract

Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal $C^*$-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph $C^*$-algebras to study the $K$-theory and gauge-invariant ideal structure of ultragraph $C^*$-algebras.

Authors

  • Takeshi KatsuraDepartment of Mathematics
    Keio University
    Yokohama, 223-8522, Japan
    e-mail
  • Paul S. MuhlyDepartment of Mathematics
    University of Iowa
    Iowa City, IA 52242-1419, U.S.A.
    e-mail
  • Aidan SimsSchool of Mathematics and Applied Statistics
    University of Wollongong
    Wollongong, NSW 2522, Australia
    e-mail
  • Mark TomfordeDepartment of Mathematics
    University of Houston
    Houston, TX 77204-3008, U.S.A.
    e-mail

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