A class of C*-algebras that are prime but not primitive

2013/06/27 by Gene Abrams, Abrams, Gene, Mark Tomforde +1
Mathematics · #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #math.OA #math.RA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1306.6669

Version II Comments: A few typos corrected. This is the version that will be published

arxiv created 2013/08/22 · arxiv updated 2013/08/26

Abstract

We establish necessary and sufficient conditions on a (not necessarily countable) graph E for the graph C*-algebra C*(E) to be primitive. Along with a known characterization of the graphs E for which C*(E) is prime, our main result provides us with a systematic method for easily producing large classes of (necessarily nonseparable) C*-algebras that are prime but not primitive. We also compare and contrast our results with similar results for Leavitt path algebras.

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• The prime spectrum and primitive ideal space of a graph C*-algebra