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We describe the primitive ideal space of the $C^{\ast}$-algebra of a row-finite $k$-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two examples. In order to do this we prove some new results on aperiodicity. Our computations indicate that when every ideal is gauge invariant, the primitive ideal space only depends on the 1-skeleton of the $k$-graph in question.Comment: 23 pages. Updated 30th June, 201

Topics:
Mathematics - Operator Algebras, 46L05, 46L55

Year: 2012

OAI identifier:
oai:arXiv.org:1105.1208

Provided by:
arXiv.org e-Print Archive

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