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arXiv · 1306.6669

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

Gene Abrams·Mark Tomforde
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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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Gene Abrams, Mark Tomforde. 2013-06-27. A class of C*-algebras that are prime but not primitive. https://arxiv.org/abs/1306.6669

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