Front: [math.OA/0106162] Simplicity of ultragraph algebras

Title: Simplicity of ultragraph algebras
Authors: Mark Tomforde
Categories: math.OA Operator Algebras
Comments: 21 pages, uses XY-pic, Version 2 comments: terminology change -- "labeled graph" was replaced by "ultragraph". Version 3 comments: some small typos corrected. Accepted for publication in the Indiana University Mathematics Journal
MSC: 46L55
Journal reference: Indiana Univ. Math. J. 52 (2003), 901--926

Abstract: 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.

Owner: Mark Tomforde
Version 1: Tue, 19 Jun 2001 18:04:47 GMT
Version 2: Fri, 19 Oct 2001 17:54:40 GMT
Version 3: Tue, 10 Jun 2003 05:06:21 GMT
Version 4: Tue, 5 Aug 2003 23:11:52 GMT