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Aperiodicity and the primitive ideal space of a row-finite $k$-graph $C^*$-algebra

Journal Article


Abstract


  • 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.

Publication Date


  • 2011

Web Of Science Accession Number


Abstract


  • 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.

Publication Date


  • 2011

Web Of Science Accession Number