Ultragraph $C^*$-algebras via topological quivers
Volume 187 / 2008
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.
