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The ideal structure of the $C\sp *$-algebras of infinite graphs

2002; Duke University Press; Volume: 46; Issue: 4 Linguagem: Inglês

10.1215/ijm/1258138472

1945-6581

Teresa Bates, Jeong Hee Hong, Iain Raeburn, Wojciech Szymański,

Advanced Topics in Algebra

We classify the gauge-invariant ideals in the $C^*$-algebras of infinite directed graphs, and describe the quotients as graph algebras. We then use these results to identify the gauge-invariant primitive ideals in terms of the structural properties of the graph, and describe the $K$-theory of the $C^*$-algebras of arbitrary infinite graphs.