The ideal structure of the C*-algebras of infinite graphs

2001/09/20 by Teresa Bates, Bates, Teresa, Jeong Hee Hong +5 · 2 citations
Mathematics · #46l05 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46l05

paper · pdf · doi:10.48550/arxiv.math/0109142

14 pages

arxiv created 2001/09/20 · arxiv updated 2009/11/30

Abstract

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.

Cited by

• On amplified graph C*-algebras as cores of Cuntz-Krieger algebras
• Relating insplittings of 2-graphs and of textile systems

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• ℕ-Graph C^*-Algebras
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures
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• Primitive ideals and pure infiniteness of ultragraph C^*-algebras