Stability of C*-algebras associated to graphs

Details Stability of C*-algebras associated to graphs Stability of C*-algebras associated to graphs

2002-05-15

arxiv.org/abs/math/0205166v2

Mathematics

Operator Algebras

9 pages

Scientific paper

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph C*-algebra. Specifically, if G is a graph and F is the graph formed by adding a head to each vertex of G, then C*(F) is the stabilization of C*(G).

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