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

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.

preprint2013arXivOpen access
Gene AbramsMark Tomforde
math.OAmath.RA
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Gene AbramsMark Tomforde

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