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

Mark Tomforde
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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.

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Mark Tomforde. 2001-10-19. A unified approach to Exel-Laca algebras and C*-algebras associated to graphs. https://arxiv.org/abs/math/0106161

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