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

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.

14 pages

References in corpus (3)

• Partial dynamical systems and C*-algebras generated by partial isometries
• Computing K-theory and Ext for graph C*-algebras
• The C*-algebras of arbitrary graphs

Cited by in corpus (14)

• Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras
• The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources
• Partial actions and KMS states on relative graph $C^{\ast }$-algebras
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Noncommutative Balls and Mirror Quantum Spheres
• Canonical traces and directly finite Leavitt path algebras
• Classifying $C^{\ast }$-algebras with both finite and infinite subquotients
• Pure infiniteness and ideal structure of $C^{\ast }$-algebras associated to Fell bundles
• Filtered K-theory for graph algebras
• On Hong and Szymanski's description of the primitive-ideal space of a graph algebra
• Strong classification of purely infinite Cuntz-Krieger algebras
• Classification of graph C*-algebras with no more than four primitive ideals
• C*-Algebras for partial product systems over N
• On the classification of nonsimple graph C*-algebras