Ultragraph C*-algebras via topological quivers

2006/11/10 by Takeshi Katsura, Paul S. Muhly, Katsura, Takeshi +5 · 3 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.math/0611318

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.

Cited by

• Groupoid and Inverse Semigroup Presentations of Ultragraph C^*-Algebras
• Minimality and effectiveness of the groupoid associated to a self-similar ultragraph
• Relative ultragraph algebras and infinite interval maps

Related

• Topological Quivers
• Quotients of Ultragraph C*-Algebras
• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs
• Primitive ideals and pure infiniteness of ultragraph C^*-algebras
• Simplicity of ultragraph algebras