Simplicity of ultragraph algebras

Details Simplicity of ultragraph algebras Simplicity of ultragraph algebras

2001-06-19

arxiv.org/abs/math/0106162v4

Indiana Univ. Math. J. 52 (2003), 901--926

Mathematics

Operator Algebras

21 pages, uses XY-pic, Version 2 comments: terminology change -- "labeled graph" was replaced by "ultragraph". Version 3 comme

Scientific paper

In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an ultragraph algebra to be purely infinite and to be AF. Using these techniques we also produce an example of an ultragraph algebra which is neither a graph algebra nor an Exel-Laca algebra. We conclude by proving that the C*-algebras of ultragraphs with no sinks are Cuntz-Pimsner algebras.

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