A unified approach to Exel-Laca algebras and C*-algebras associated to graphs

Abstract

We define an ultragraph, which is a generalization of a directed graph, and describe how to associate a C*-algebra to it. We show that the class of ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca algebras. We also show that many of the techniques used for graph algebras can be applied to ultragraph algebras and that the ultragraph provides a useful tool for analyzing Exel-Laca algebras. Our results include versions of the Cuntz-Krieger Uniqueness Theorem and the Gauge-Invariant Uniqueness Theorem for ultragraph algebras.

arXiv comment22 pages, uses XY-pic, New version comments: terminology change - "labeled graph" was replaced by "ultragraph", to appear in JOT

References in corpus (1)

• Computing K-theory and Ext for graph C*-algebras

Cited by in corpus (11)

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• $C^{\ast }$-algebras of labelled graphs III - $K$-theory computations
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• Topological full groups of ultragraph groupoids as an isomorphism invariant
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• Realizing ultragraph Leavitt path algebras as Steinberg algebras
• Topological freeness for $C^{\ast }$-correspondences
• Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States
• Primitive Ideals of Labelled Graph $C^{\ast }$-algebras
• Prime and Primitive Ideals of Ultragraph Leavitt Path Algebras
• The simplicity of the C*-algebras associated to arbitrary labeled spaces