TY - JOUR

T1 - A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras III, ideal structures

AU - Katsura, Takeshi

N1 - Copyright:
Copyright 2006 Elsevier B.V., All rights reserved.

PY - 2006/12

Y1 - 2006/12

N2 - We investigate the ideal structures of the C*-algebras arising from topological graphs. We give a complete description of ideals of such C*-algebras that are invariant under the so-called gauge action, and give a condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C*-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph for which the associated C*-algebra is prime but not primitive.

AB - We investigate the ideal structures of the C*-algebras arising from topological graphs. We give a complete description of ideals of such C*-algebras that are invariant under the so-called gauge action, and give a condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C*-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph for which the associated C*-algebra is prime but not primitive.

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U2 - 10.1017/S0143385706000320

DO - 10.1017/S0143385706000320

M3 - Article

AN - SCOPUS:33751033805

VL - 26

SP - 1805

EP - 1854

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 6

ER -